   Chapter 3.5, Problem 62E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find f′(x). Check that your answer is reasonable by comparing the graphs of f and f′.62. f(x) = arctan(x2 – x)

To determine

To find: The derivative of the function and to check the derivative f(x), f(x) is reasonable by comparing the graph of f(x) and f(x).

Explanation

Given:

The function is f(x)=arctan(x2x).

Derivative rules:

(1) Chain rule: dydx=dydududx

(2) Derivative of the inverse trigonometric function: ddx(tan1(x))=11+x2.

(3) Quotient rule: ddx(fg)=gddx(f)fddx(g)g2

Calculation:

Obtain the derivative of the function.

Consider the function f(x)=arctan(x2x)

Differentiate the function implicitly with respect to t,

f(x)=ddx(arctan(x2x))

Let u=x2x.

f(x)=ddx(arctan(u))

Apply the chain rule (1) and derivative rule (2),

f(x)=ddu(arctan(u))dudx=[11+u2]dudx

Substitute u=x2x

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