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Chapter 2: Q. 54 (page 222)

Use logarithmic differentiation to find the derivatives of each of the functions in Exercises 49鈥�58.

f(x)=2x+13x

Short Answer

Expert verified

The derivative of function isy'=2x+13x6x2x+1+3ln(2x+1)x

Step by step solution

01

Step 1. Given Information

The given function isf(x)=2x+13x

02

Step 2. Calculation    

First, we will take the log on both sides and then differentiate it,

lny=ln2x+13xlny=3x路ln(2x+1)1yy'=3x2x+12+ln(2x+1)x3y'=2x+13x6x2x+1+3ln(2x+1)x

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Most popular questions from this chapter

For each function graphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

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(a) In real-world terms, what does T(5)represent and what are its units? What does T'(5)represent and what are its units?

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Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

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Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x-12(x2-1)3
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