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Chapter 2: Q 36. (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.

fx=lnx2+1

Short Answer

Expert verified

The required answer isxx2+1lnx2+1.

Step by step solution

01

Step 1. Given information.

The given function is:

fx=lnx2+1

02

Step 2. Find the derivative of the given function.

fx=lnx2+1f'x=ddxlnx2+1=12lnx2+1路1x2+1路2x=xx2+1lnx2+1

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Most popular questions from this chapter

State the chain rule for differentiating a composition g(h(x))of two functions expressed

(a) in 鈥減rime鈥� notation and

(b) in Leibniz notation.

Suppose u(x)=3x2+1and f(u)=u2+3u51-u. Use the chain rule to find role="math" localid="1648356625815" ddx(f(u(x))) without first finding the formula for f(u(x)).

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that passes through the point (3,2)and is parallel to the tangent line to f(x)=1x at x=-1.

Use the definition of the derivative to prove the following special case of the product rule

ddx(x2f(x))=2xf(x)+x2f'(x)

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=7x2+8x11-18;f(0)=-2
See all solutions

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