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10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 5.5, Problem 43E

Textbook Problem

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Finding a Derivative In Exercises 37-58, find the derivative of the function. (Hint: In some exercises, you may find it helpful to apply logarithmic properties before differentiating.)

To determine

**To calculate:** The derivative of the function

**Given:**

The provided function is

**Formula used:**

The product rule of differentiation states that

The derivative of function

**Calculation:**

Consider the function,

Differentiate both sides with respect to *t*,

Recall the product rule

Calculus

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Prove...Ch. 5.3 - Proof Prove that if f has an inverse function,...Ch. 5.3 - Proof Prove that if a function has an inverse...Ch. 5.3 - Proof Prove that a function has an inverse...Ch. 5.3 - Using Theorem 5.7 Is the converse of the second...Ch. 5.3 - Derivative of an Inverse Function Show that...Ch. 5.3 - Derivative of an Inverse FunctionShow that...Ch. 5.3 - Derivative of an Inverse FunctionShow that...Ch. 5.3 - Inverse Function Let f(x)=x2x1 Show that f is its...Ch. 5.3 - Using a Function Let f(x)=ax+bcx+d (a) Show that f...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Solving an Exponential or Logarithmic Equation In...Ch. 5.4 - Sketching a Graph In Exercises 19-24, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 17-22, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 17-22, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 17-22, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 19-24, sketch the...Ch. 5.4 - Sketching a Graph In Exercises 19-24, sketch the...Ch. 5.4 - 23. Comparing Graphs Use a graphing utility to...Ch. 5.4 - Asymptotes Use a graphing utility to graph the...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Matching In Exercises 2528, match the equation...Ch. 5.4 - Inverse Functions In Exercises 29-32, illustrate...Ch. 5.4 - Inverse Functions In Exercises 2932, illustrate...Ch. 5.4 - Inverse Functions In Exercises 2932, illustrate...Ch. 5.4 - Inverse Functions In Exercises 2932, illustrate...Ch. 5.4 - Finding a Derivative In Exercises 3354, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding a Derivative In Exercises 33-54, find the...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.4 - Implicit Differentiation In Exercises 63 and 64,...Ch. 5.4 - Implicit Differentiation In Exercises 63 and 64,...Ch. 5.4 - Finding the Equation of a Tangent Line In...Ch. 5.4 - Finding the Equation of a Tangent Line In...Ch. 5.4 - Finding a Second Derivative In Exercises 67 and...Ch. 5.4 - Finding a Second Derivative In Exercises 67 and...Ch. 5.4 - Differential Equation In Exercises 69 and 70, show...Ch. 5.4 - Differential Equation In Exercises 69 and 70, show...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Finding Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Relative Extrema and Points of Inflection In...Ch. 5.4 - Area Find the area of the largest rectangle that...Ch. 5.4 - Area Perform the following steps to find the...Ch. 5.4 - Finding an Equation of a Tangent Line Find point...Ch. 5.4 - HOW DO YOU SEE IT? The figure shows the graphs of...Ch. 5.4 - Depreciation The value V of an item t years after...Ch. 5.4 - Harmonic Motion The displacement from equilibrium...Ch. 5.4 - Atmospheric Pressure A meteorologist measures the...Ch. 5.4 - Modeling Data The table lists the approximate...Ch. 5.4 - Linear and Quadratic Approximation In Exercises 87...Ch. 5.4 - Linear and Quadratic Approximation In Exercises 87...Ch. 5.4 - Stirlings Formula For large values of n,...Ch. 5.4 - Stirling's Formula For large values of n, n! = 1 ...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite IntegralIn Exercises 91108,...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite IntegralIn Exercises 91108,...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Finding an Indefinite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite IntegralIn Exercises 109118,...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Evaluating a Definite Integral In Exercises...Ch. 5.4 - Slope Field In Exercises 119 and 120, a...Ch. 5.4 - Slope FieldIn Exercises 119 and 120, a...Ch. 5.4 - Differential Equation In Exercises 121 and 122,...Ch. 5.4 - Differential Equation In Exercises 119 and 120,...Ch. 5.4 - Differential Equation In Exercises 121 and 122,...Ch. 5.4 - Differential Equation In Exercises 121 and 122,...Ch. 5.4 - AreaIn Exercises 125128, find the area of the...Ch. 5.4 - Area In Exercises 123-126, find the area of the...Ch. 5.4 - Area In Exercises 123-126, find the area of the...Ch. 5.4 - Area In Exercises 123-126, find the area of the...Ch. 5.4 - Midpoint Rule In Exercises 127 and 128, use the...Ch. 5.4 - Midpoint Rule In Exercises 127 and 128, use the...Ch. 5.4 - Probability A car battery has an average lifetime...Ch. 5.4 - Probability The median waiting time (in minutes)...Ch. 5.4 - Modeling Data A valve on a storage tank is opened...Ch. 5.4 - Using the Area of a Region Find the value of a...Ch. 5.4 - WRITING ABOUT CONCEPTS Properties of the Natural...Ch. 5.4 - A Function and Its Derivative Is there a function...Ch. 5.4 - Choosing a Function Without integrating, state the...Ch. 5.4 - Analyzing a Graph Consider the function...Ch. 5.4 - Deriving an Inequality Given ex1 for x0, it...Ch. 5.4 - 141. Horizontal Motion The position function of a...Ch. 5.4 - Analyzing a Function Let f(x)=lnxx. (a) Graph f on...Ch. 5.4 - Solving an Equation Find, to three decimal places,...Ch. 5.4 - Finding the Maximum Rate of Change Verify that the...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Evaluating a Logarithmic Expression In Exercises...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Exponential and Logarithmic Forms of Equations In...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Sketching a Graph In Exercises 15-20, sketch the...Ch. 5.5 - Matching In Exercises 15–18, match the function...Ch. 5.5 - MatchingIn Exercises 1518, match the function with...Ch. 5.5 - MatchingIn Exercises 1518, match the function with...Ch. 5.5 - Matching In Exercises 15–18, match the function...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 19–24, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 21-26, solve for...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 25–34, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Solving an Equation In Exercises 2534, solve the...Ch. 5.5 - Solving an Equation In Exercises 27-36, solve the...Ch. 5.5 - Inverse Functions In Exercises 37 and 38,...Ch. 5.5 - Inverse Functions In Exercises 37 and 38,...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 37-58, find the...Ch. 5.5 - Finding a Derivative In Exercises 37-58, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 37-58, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding a Derivative In Exercises 39-60, find the...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Logarithmic Differentiation In Exercises 65-68,...Ch. 5.5 - Finding an Equation of a Tangent LineIn Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 71–78,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 7178,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Finding an Indefinite Integral In Exercises 69-76,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 77-80,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 77-80,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 77-80,...Ch. 5.5 - Evaluating a Definite Integral In Exercises 7982,...Ch. 5.5 - Area In Exercises 83 and 84, find the area of the...Ch. 5.5 - Area In Exercises 83 and 84, find the area of the...Ch. 5.5 - Analyzing a Logarithmic Equation Consider the...Ch. 5.5 - Comparing Rates of Growth Order the functions...Ch. 5.5 - Inflation When the annual rate of inflation...Ch. 5.5 - Depreciation After t years, the value of a car...Ch. 5.5 - Compound Interest In Exercises 89-92, complete the...Ch. 5.5 - Compound Interest In Exercises 89-92, complete the...Ch. 5.5 - Compound Interest In Exercises 89–92, complete the...Ch. 5.5 - Compound Interest In Exercises 89-92, complete the...Ch. 5.5 - Compound Interest In Exercises 93–96, complete the...Ch. 5.5 - Compound Interest In Exercises 9396, complete the...Ch. 5.5 - Compound Interest In Exercises 93-96, complete the...Ch. 5.5 - Compound Interest In Exercises 93-96, complete the...Ch. 5.5 - Compound Interest Assume that you can earn 6% on...Ch. 5.5 - Compound Interest Consider a deposit of $100...Ch. 5.5 - Timber Yield The yield V (in millions of cubic...Ch. 5.5 - HOW DO YOU SEE IT? The graph shows the proportion...Ch. 5.5 - Population Growth A lake is stocked with 500 fish,...Ch. 5.5 - Modeling Data The breaking strengths B (in tons)...Ch. 5.5 - 103. Comparing Models The numbers y of pancreas...Ch. 5.5 - An Approximation of e Complete the table to...Ch. 5.5 - Modeling Data In Exercises 105 and 106, find an...Ch. 5.5 - Modeling Data In Exercises 105 and 106, find an...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - Using Properties of Exponents In Exercises...Ch. 5.5 - True or False? In Exercises 111–116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - True or False? In Exercises 111116, determine...Ch. 5.5 - Comparing Functions (a) Show that (23)22(32). (b)...Ch. 5.5 - Finding an inverse Function Let f(x)=ax1ax+1. for...Ch. 5.5 - Logistic Differential Equation Show that solving...Ch. 5.5 - Using Properties of Exponents function f(x)=ax,...Ch. 5.5 - Tangent Lines (a) Determine y' given yx=xy. (b)...Ch. 5.5 - Which is greater (n)n+1 or (n+1)n where n8?Ch. 5.5 - Show that if x is positive, then loge(1+1x)11+xCh. 5.6 - Restricted Domain What is a restricted domain? Why...Ch. 5.6 - Finding Coordinates In Exercises 5 and 6,...Ch. 5.6 - Finding Coordinates In Exercises 5 and 6,...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Evaluating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Approximating Inverse Trigonometric Functions In...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Using a Right Triangle In Exercises 19-24, use the...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Evaluating an Expression In Exercises 25-28,...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right TriangleIn...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Simplifying an Expression Using a Right Triangle...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Solving an Equation In Exercises 37-40, solve the...Ch. 5.6 - Verifying Identities In Exercises 81 and 82,...Ch. 5.6 - Verifying Identities In Exercises 81 and 82,...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding a Derivative In Exercises 41-56, find the...Ch. 5.6 - Finding a Derivative In Exercises 3958, find the...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding an Equation of a Tangent Line In Exercises...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Finding Relative Extrema In Exercises 63-66, find...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Analyzing an Inverse Trigonometric Graph In...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Implicit Differentiation In Exercises 71-74, use...Ch. 5.6 - Finding Values (a) Use a graphing utility to...Ch. 5.6 - HOW DO YOU SEE IT? The graph of g(x) = cos x is...Ch. 5.6 - Inverse Trigonometric Functions Explain why tan =0...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 83-86, determine...Ch. 5.6 - True or False? In Exercises 8590, determine...Ch. 5.6 - True or False? In Exercises 8590, determine...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Linear and Quadratic Approximations In Exercises...Ch. 5.6 - Angular Rate of Change An airplane flies at an...Ch. 5.6 - Writing Repeat Exercise 87 for an altitude of 3...Ch. 5.6 - Angular Rate of Change In a free-fall experiment,...Ch. 5.6 - Angular Rate of Change A television camera at...Ch. 5.6 - Maximizing an Angle A billboard 85 feet wide is...Ch. 5.6 - Angular Speed A patrol car is parked 50 feet from...Ch. 5.6 - Proof (a) Prove that...Ch. 5.6 - Proof Prove each differentiation formula. (a)...Ch. 5.6 - Describing a Graph Use a graphing utility to graph...Ch. 5.6 - Think About It Use a graphing utility to graph...Ch. 5.6 - Maximizing an Angle In the figure, find the value...Ch. 5.6 - Finding a Distance In the figure, find PR such...Ch. 5.6 - Proof Prove that arcsinx=arctan(x1x2),x1.Ch. 5.6 - Inverse Secant Function Some calculus textbooks...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 120,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Finding an Indefinite Integral In Exercises 3-22,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 2132,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 2334,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Evaluating a Definite Integral In Exercises 23-34,...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 35-42, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Completing the Square In Exercises 3342, find or...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Integration by Substitution In Exercises 43-46,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Comparing Integration Problems In Exercises 47-50,...Ch. 5.7 - Finding an Integral Decide whether you can find...Ch. 5.7 - HOW DO YOU SEE IT? 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