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Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248

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Chapter
Section
BuyFindarrow_forward

Applied Calculus

7th Edition
Waner + 1 other
Publisher: Cengage Learning,
ISBN: 9781337291248
Chapter 4.5, Problem 27E
Textbook Problem
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In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.]

g ( x ) = ln ( x 2 2.1 x 0.3 )

To determine

To calculate: The derivative of the function g(x)=ln(x22.1x0.3).

Explanation of Solution

Given information:

The provided function is g(x)=ln(x22.1x0.3).

Formula used:

The derivative of natural logarithm of a function is ddx(lnu)=1ududx.

Constant multiple rule of derivative of function f(x) is f(cx)=cf(x) where c is constant.

The derivative of the function using power rule, y=xn is dydx=nxn1.

Calculation:

Consider the provided function g(x)=ln(x22.1x0.3),

The derivative of natural logarithm of a function is ddx(lnu)=1ududx.

To calculate the derivative of the function g(x)=ln(x22.1x0.3), apply the derivative of natural logarithm of a function is ddx(lnu)=1ududx.

Here, u=x22.1x0.3

Then, the derivative of function is,

g(x)=[ddxln(x22.1x0.3)][=1(x22.1x0

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Applied Calculus
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In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 1-66, find the derivative of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 67-72, find the equation of the...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - In Exercises 73-78, use lHospitals rule to find...Ch. 4.5 - Research and Development: Industry The total spent...Ch. 4.5 - Research and Development: Federal The total spent...Ch. 4.5 - Research and Development: Industry (Refer to...Ch. 4.5 - Research and Development: Federal (Refer to...Ch. 4.5 - Carbon Dating The age in years of a specimen that...Ch. 4.5 - Iodine Dating The age in years of a specimen that...Ch. 4.5 - New York City Housing Costs: Downtown The average...Ch. 4.5 - New York City Housing Costs: Uptown The average...Ch. 4.5 - Big Brother The following chart shows the total...Ch. 4.5 - Big Brother The following chart shows the total...Ch. 4.5 - Investments If $10,000 is invested in a savings...Ch. 4.5 - Investments If $20,000 is invested in a savings...Ch. 4.5 - Investments If $10,000 is invested in a savings...Ch. 4.5 - Investments If $20,000 is invested in a savings...Ch. 4.5 - The 2003 SARS Outbreak In the early stages of the...Ch. 4.5 - The 2003 SARS Outbreak A few weeks into the deadly...Ch. 4.5 - The 2014 Ebola Outbreak In the first 6 months of...Ch. 4.5 - The 2014 Ebola Outbreak In the first 6 months of...Ch. 4.5 - SAT Scores by Income The following bar graph shows...Ch. 4.5 - SAT Scores by Income The following bar graph shows...Ch. 4.5 - Demographics: Average Age and Fertility The...Ch. 4.5 - Demographics: Average Age and Fertility The...Ch. 4.5 - Epidemics A flu epidemic described in Example 1 in...Ch. 4.5 - Epidemics Another epidemic follows the curve...Ch. 4.5 - Subprime Mortgages during the Housing Bubble...Ch. 4.5 - Subprime Mortgage Debt during the Housing Bubble...Ch. 4.5 - Subprime Mortgages during the Housing Bubble...Ch. 4.5 - Subprime Mortgage Debt during the Housing Bubble...Ch. 4.5 - Population Growth The population of Lower Anchovia...Ch. 4.5 - Population Growth The population of Upper Anchovia...Ch. 4.5 - Radioactive Decay Plutonium 239 has a half-life of...Ch. 4.5 - Radioactive Decay Carbon 14 has a half-life of...Ch. 4.5 - Cellphone Revenues The number of cellphone...Ch. 4.5 - Cellphone Revenues The annual revenue for...Ch. 4.5 - Complete the following: The derivative of e raised...Ch. 4.5 - Complete the following: The derivative of the...Ch. 4.5 - Complete the following: The derivative of 2 raised...Ch. 4.5 - Complete the following: The derivative of the base...Ch. 4.5 - What is wrong with the following?...Ch. 4.5 - What is wrong with the following? ddx22x=(2)22x X...Ch. 4.5 - What is wrong with the following? ddx32x=(2x)32x1...Ch. 4.5 - What is wrong with the following? ddxln(3x21)=16x...Ch. 4.5 - The number N of music downloads on campus is...Ch. 4.5 - The number N of graphing calculators sold on...Ch. 4.5 - Show that the fractional rate of change of the...Ch. 4.5 - Show that the fractional rate of change of f(x) is...Ch. 4.5 - Let A(t) representa quantity growing...Ch. 4.5 - Let A(t) be the amount of money in an account that...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 110, find dy/dx, using implicit...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 11-30, find the indicated derivative...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 3142, use implicit differentiation to...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - In Exercises 43-52, use logarithmic...Ch. 4.6 - Productivity The number of CDs per hour that...Ch. 4.6 - Productivity The number of cellphone accessory...Ch. 4.6 - Demand The demand equation for soccer tournament...Ch. 4.6 - Cost Equations The cost C (in cents) of producing...Ch. 4.6 - Housing Costs61 The cost C (in dollars) of...Ch. 4.6 - Employment An employment research company...Ch. 4.6 - Grades62 A productivity formula for a students...Ch. 4.6 - Grades Repeat Exercise 59 using the following...Ch. 4.6 - Exercises 61 and 62 are based on the following...Ch. 4.6 - Exercises 61 and 62 are based on the following...Ch. 4.6 - Fill in the missing terms: The equation x=y3+y3...Ch. 4.6 - Fill in the missing terms: When x0 in the equation...Ch. 4.6 - Use logarithmic differentiation to give another...Ch. 4.6 - Use logarithmic differentiation to give a proof of...Ch. 4.6 - If y is given explicitly as a function of x by an...Ch. 4.6 - Explain why one should not expect dy/dx tobe a...Ch. 4.6 - If y is a function of x and dy/dx0 atsome point,...Ch. 4.6 - If you are given an equation in x and y such that...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 1-32, find the derivative of the...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 33-40, find all values of x (if any)...Ch. 4 - In Exercises 41-46, find dy/dx for the given...Ch. 4 - In Exercises 41-46, find dy/dx for the given...Ch. 4 - In Exercises 41-46, find dy/dx for the given...Ch. 4 - In Exercises 41-46, find dy/dx for the given...Ch. 4 - In Exercises 41-46, find dy/dx for the given...Ch. 4 - In Exercises 41-46, find dy/dx for the given...Ch. 4 - In Exercises 47-52, find the equation of the...Ch. 4 - In Exercises 47-52, find the equation of the...Ch. 4 - In Exercises 47-52, find the equation of the...Ch. 4 - In Exercises 47-52, find the equation of the...Ch. 4 - In Exercises 47-52, find the equation of the...Ch. 4 - In Exercises 47-52, find the equation of the...Ch. 4 - In Exercises 53-56, find the limit: limx+x2ex2Ch. 4 - In Exercises 53-56, find the limit: limxxexCh. 4 - In Exercises 53-56, find the limit: limx0x2ex21Ch. 4 - In Exercises 53-56, find the limit:...Ch. 4 - Sales OHaganBooks.com fits the cubic curve...Ch. 4 - Rising Sea Level Marjory Duffin is still toying...Ch. 4 - Cost As OHaganBooks.coms sales increase, so do its...Ch. 4 - Cost OHaganBooks.com has been experiencing a run...Ch. 4 - Revenue At the moment, OHaganBooks.com is selling...Ch. 4 - Revenue Because of ongoing problems with its large...Ch. 4 - Percentage Rate of Change of Revenue The...Ch. 4 - P/E Ratios At the beginning of last week,...Ch. 4 - P/E Ratios Refer to Exercise 64. Jay Campbell, who...Ch. 4 - Percentage Rate of Change of P/E Ratios Refer to...Ch. 4 - Sales OHaganBooks.com decided that the cubic curve...Ch. 4 - Rising Sea Level Upon some reflection, Marjory...Ch. 4 - Website Activity The number of hits on...Ch. 4 - Website Activity The number of hits on...Ch. 4 - Demand and Revenue The price p that...Ch. 4 - Demand and Revenue The price p that...Ch. 4 - Find limt+N(t) forboth models, and interpret the...

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