   Chapter 5, Problem 50RE ### 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. y = ∫ 2 x 3 x + 1 sin ( t 4 )   d t

To determine

To calculate: The derivative of the function y.

Explanation

Given information:

The function is y=2x3x+1sin(t4)dt (1)

Consider u=2x (2)

Differentiate both sides of the Equation (2).

dudx=ddx(2x)=2

Consider v=3x+1 (3)

Differentiate both sides of the Equation (3).

dvdx=ddx(3x+1)=3

Apply Chain rule:

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

Rearrange the Equation (1) using Chain rule.

y=2x0sin(t4)dt+03x+1sin(t4)dt (5)

The expression to find the derivative of the function by using Equation (5) as shown below.

Substitute u for 2x and v for 3x+1 in Equation (5).

ddx(y)=ddx(u0sin(t4)dt+0vsin(t4)dt)=ddu(u0sin(t4

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