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Chapter 2: Q 37. (page 222)

Find the derivatives of each of functions in Exercises 17鈥�44. In some cases it may be convenient to do some preliminary algebra.

f(x)=lnx2+ex

Short Answer

Expert verified

The required answer is1x2+ex2x+ex12x-12.

Step by step solution

01

Step 1. Given information.

The given function is:

f(x)=lnx2+ex

02

Step 2. Find the derivative of the given function.

f(x)=lnx2+exf'(x)=ddxlnx2+ex=1x2+exddxx2+ex=1x2+ex2x+ex路ddxx=1x2+ex2x+ex路12x-12=1x2+ex2x+ex12x-12

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Most popular questions from this chapter

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23鈥�38.

24.f(x)=x3,x=1

Use the definition of the derivative to find ffor each function fin Exercises 39-54.

f(x)=x2-1x2-x-2

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

For each function f and value x=cin Exercises 35鈥�44, use a sequence of approximations to estimate f'(c). Illustrate your work with an appropriate sequence of graphs of secant lines.

f(x)=4-x2,c=1

For each function fgraphed 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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