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10th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285057095

Chapter 2.4, Problem 59E

Textbook Problem

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Finding a Derivative In Exercises 43–64, find the derivative of the function.

To determine

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

**Given:**

The function is

**Formula used:**

The chain rule of differentiation states that,

The derivative of the secant function is

The power rule states that,

**Calculation:**

Consider the function,

Differentiate the function with respect to *t*,

Recall the chain rule of differentiation,

Here

So,

With the help of power ru

Calculus

Show all chapter solutions

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Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Finding a Second Derivative In Exercises 91-100....Ch. 2.3 - Finding a Higher-Order Derivative In Exercises...Ch. 2.3 - Finding a Higher-Order Derivative In Exercises...Ch. 2.3 - Finding a Higher-Order Derivative In Exercises...Ch. 2.3 - Finding a Higher-Order Derivative In Exercises...Ch. 2.3 - Using Relationships In Exercises 105-108. use the...Ch. 2.3 - Using Relationships In Exercises 105-108. use the...Ch. 2.3 - Using Relationships In Exercises 105-108, use the...Ch. 2.3 - Using Relationships In Exercises 105-108. use the...Ch. 2.3 - Sketching a Graph Sketch the graph of a...Ch. 2.3 - Sketching a Graph Sketch the graph of a...Ch. 2.3 - Identifying Graphs In Exercises 111 and 112, the...Ch. 2.3 - Identifying Graphs In Exercises 111 and 112, the...Ch. 2.3 - Sketching Graphs In Exercises 113 and 114, the...Ch. 2.3 - Sketching Graphs In Exercises 111114, the graph of...Ch. 2.3 - Sketching Graphs In Exercises 113 and 114, the...Ch. 2.3 - Sketching Graphs In Exercises 111114, the graph of...Ch. 2.3 - Acceleration The velocity of an object is...Ch. 2.3 - Acceleration The velocity of an automobile...Ch. 2.3 - Stopping Distance A car is traveling at a rate of...Ch. 2.3 - HOW DO YOU SEE IT? The figure shows the graphs of...Ch. 2.3 - Finding a Pattern In Exercises 121 and 122,...Ch. 2.3 - Finding a Pattern In Exercises 121 and 122....Ch. 2.3 - Finding a Pattern Consider the function...Ch. 2.3 - Finding a Pattern Develop a general rule for the...Ch. 2.3 - Finding a Pattern In Exercises 125 and 126, find...Ch. 2.3 - Finding a Pattern In Exercises 125 and 126, find...Ch. 2.3 - Differential Equations In Exercises 127130, verify...Ch. 2.3 - Differential Equations In Exercises 127-130,...Ch. 2.3 - Differential Equations In Exercises 127-130,...Ch. 2.3 - Differential Equations In Exercises 127-130,...Ch. 2.3 - True or False? In Exercises 131-136, determine...Ch. 2.3 - True or False? In Exercises 131-136. determine...Ch. 2.3 - True or False? In Exercises 131-136. determine...Ch. 2.3 - True or False? In Exercises 129134, determine...Ch. 2.3 - True or False? In Exercises 131-136, determine...Ch. 2.3 - True or False? 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Describing Relationships Describe the relationship...Ch. 2.4 - Think about It The table shows some values of the...Ch. 2.4 - Using Relationships Given that g(5)=3,g(5)=6,...Ch. 2.4 - Finding Derivatives In Exercises 99 and 100, the...Ch. 2.4 - Finding Derivatives In Exercises 99 and 100, the...Ch. 2.4 - Doppler Effect The frequency F of a fire truck...Ch. 2.4 - Harmonic Motion The displacement from equilibrium...Ch. 2.4 - Pendulum A 15-centimeter pendulum moves according...Ch. 2.4 - Wave Motion A buoy oscillates in simple harmonic...Ch. 2.4 - Modeling Data The normal daily maximum...Ch. 2.4 - HOW DO YOU SEE IT? The cost C (in dollars) of...Ch. 2.4 - Biology The number N of bacteria in a culture...Ch. 2.4 - Depreciation The value V of a machine t years...Ch. 2.4 - Finding a Pattern Consider the function f(x)=sinx,...Ch. 2.4 - Conjecture Let f be a differentiable function of...Ch. 2.4 - Think About It Let r(x)=f(g(x)) and s(x)=g(f(x)),...Ch. 2.4 - Using Trigonometric Functions (a) Find the...Ch. 2.4 - Even and Odd Functions (a) Show that the...Ch. 2.4 - Proof Let u be a differentiable function of x. Use...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Using Absolute Value In Exercises 115-118. use the...Ch. 2.4 - Linear and Quadratic Approximations The linear and...Ch. 2.4 - Linear and Quadratic Approximations The linear and...Ch. 2.4 - True or False? In Exercises 125128, determine...Ch. 2.4 - True or False? 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Use the graph to answer the...Ch. 2.5 - Finding Equations of Tangent Lines Consider the...Ch. 2.5 - Tangent Lines and Intercepts Let l. be any tangent...Ch. 2.5 - Proof (a) Prove (Theorem 3.3) that d/dxxn=nxn1 for...Ch. 2.5 - Slope Find all points on the circle x2+y2=100...Ch. 2.5 - Tangent Lines Find equations of both tangent lines...Ch. 2.5 - Normals to a Parabola The graph shows die normal...Ch. 2.5 - Normal Lines (a) Find an equation of the normal...Ch. 2.6 - Related Rates In your own words, state the...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Using Related Rates In Exercises 3-6, assume that...Ch. 2.6 - Moving Point In Exercises 7-10, a point is moving...Ch. 2.6 - Moving Point In Exercises 7-10, a point is moving...Ch. 2.6 - Moving Point In Exercises 710, a point is moving...Ch. 2.6 - Moving Point In Exercises 7-10, a point is moving...Ch. 2.6 - WRITING ABOUT CONCEPTS Related Rates Consider the...Ch. 2.6 - Area The radius r of a circle is increasing at a...Ch. 2.6 - 12. 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Volume The surface area of a cube with sides...Ch. 2 - Vertical Motion In Exercises 27 and 28, use the...Ch. 2 - Vertical Motion In Exercises 27 and 28, use the...Ch. 2 - Finding a Derivative In Exercises 29-42, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 2940, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 29-42, use the...Ch. 2 - Finding a Derivative In Exercises 2940, use the...Ch. 2 - Finding a Derivative In Exercises 29-40, use the...Ch. 2 - Finding a Derivative In Exercises 2940, use the...Ch. 2 - Finding an Equation of a Tangent Line In Exercises...Ch. 2 - Finding an Equation of a Tangent Line In Exercises...Ch. 2 - Finding an Equation of a Tangent Line In Exercises...Ch. 2 - Finding an Equation of a Tangent Line In...Ch. 2 - Finding a Second Derivative In Exercises 45-50,...Ch. 2 - Finding a Second Derivative In Exercises 45-50,...Ch. 2 - Finding a Second Derivative In Exercises 45-50,...Ch. 2 - Finding a Second Derivative In Exercises 45-50,...Ch. 2 - Finding a Second Derivative In Exercises 45-50,...Ch. 2 - Finding a Second Derivative In Exercises 45-50,...Ch. 2 - Acceleration The velocity of an object in meters...Ch. 2 - Acceleration The velocity of an automobile...Ch. 2 - Find a Derivative In Exercise 53- 64, find the...Ch. 2 - Find a Derivative In Exercise 53- 64, find the...Ch. 2 - Finding a Derivative In Exercises 5364, find the...Ch. 2 - Finding a Derivative In Exercises 53-64, find the...Ch. 2 - Finding a Derivative In Exercises 53-64, find the...Ch. 2 - Finding a Derivative In Exercises 5364, find the...Ch. 2 - Finding a Derivative In Exercises 53-64, find the...Ch. 2 - Finding a Derivative In Exercises 53-64, find the...Ch. 2 - Finding a Derivative In Exercises 53-64, find the...Ch. 2 - Finding a Derivative In Exercises 53-64, find the...Ch. 2 - Finding a Derivative In Exercises 5364, find the...Ch. 2 - Finding a Derivative In Exercises 53-64, find the...Ch. 2 - Finding a Derivative In Exercises 65-70, find and...Ch. 2 - Finding a Derivative InExercises 65-70, find and...Ch. 2 - Finding a Derivative In Exercises 65-70, find and...Ch. 2 - Finding a Derivative InExercises 65-70, find and...Ch. 2 - Finding a Derivative InExercises 65-70, find and...Ch. 2 - Finding a Derivative In Exercises 65-70, find and...Ch. 2 - Finding the Second Derivative InExercises 71-74,...Ch. 2 - Finding a Second Derivative In Exercises 71-74,...Ch. 2 - Finding a Second Derivative In Exercises 71-74,...Ch. 2 - Finding a Second Derivative In Exercises 7174,...Ch. 2 - 75. Refrigeration The temperature T (in degrees...Ch. 2 - Harmonic Motion The displacement from equilibrium...Ch. 2 - Finding a Derivative In Exercises 77-82, find...Ch. 2 - Finding a Derivative In Exercises 77-82, find...Ch. 2 - Finding a Derivative In Exercises 77-82, find...Ch. 2 - Finding a Derivative In Exercises 77-82, find...Ch. 2 - Finding a Derivative In Exercises 77-82, find...Ch. 2 - Finding a Derivative In Exercises 77-82, find...Ch. 2 - Tangent Lines and Normal Lines In Exercises 83 and...Ch. 2 - Tangent Lines and Normal Lines In Exercises 83-84,...Ch. 2 - Rate of Change A point moves along the curve y=x...Ch. 2 - Surface Area All edges of a cube are expanding at...Ch. 2 - Linear vs. Angular Speed A rotating beacon is...Ch. 2 - Moving Shadow A sandbag is dropped from a balloon...Ch. 2 - Finding Equations of Circles Consider the graph of...Ch. 2 - Finding Equations of Tangent Lines Graph the two...Ch. 2 - Finding a Polynomial Find a third-degree...Ch. 2 - Finding a Function Find a function of the form...Ch. 2 - Tangent Lines and Normal Lines (a) Find an...Ch. 2 - Finding Polynomials (a) Find the polynomial...Ch. 2 - Famous Curve The graph of the eight curve...Ch. 2 - Famous Curve The graph of the pear-shaped quartic...Ch. 2 - Shadow Length A man 6 feet tall walks at a rate of...Ch. 2 - Moving Point A particle is moving along the graph...Ch. 2 - Projectile Motion An astronaut standing on the...Ch. 2 - Proof Let E be a function satisfying E(0)=E(0)=1....Ch. 2 - Proof Let L be a differentiable function for all...Ch. 2 - Radians and Degrees The fundamental limit...Ch. 2 - Acceleration and Jerk If a is the acceleration of...

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