   Chapter 5, Problem 48RE ### 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 the derivative of the function. g ( x ) = ∫ 0 sin x 1 − t 2 1 + t 4   d t

To determine

To calculate: The derivative of the function.

Explanation

Given information:

The function is g(x)=1sinx1t21+t4dt (1)

Calculation:

Consider sinx as u as shown below:

u=sinx (2)

Differentiate on both sides of the above equation.

dudx=cosx (3)

By Chain rule:

ddx[F(g(x))]=F(g(x))g(x) (4)

The expression to find the derivative of the given function by using Equation (4) is shown below:

ddx(1sinx1t21+t4dt)=ddx(1u1t21+t4dt)=ddu(1u

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