   Chapter 3.1, Problem 30E ### 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

# Differentiate the function. D ( t ) = 1 + 16 t 2 ( 4 t ) 3

To determine

To find: The derivative of the function D(t)=1+16t2(4t)3.

Explanation

Given:

The function, D(t)=1+16t2(4t)3.

Formula used:

The Constant Multiple Rule:

If c is a constant and f(t) is a differentiable function, then the constant multiple rule is,

ddt[cf(t)]=cddtf(t) (1)

The Power Rule:

If n is any real number, then the power rule is,

ddt(tn)=ntn1 (2)

The Sum Rule:

If f(t) and g(t) are both differentiable functions, then the sum rule is,

ddt[f(t)+g(t)]=ddt[f(t)]+ddt[g(t)] (3)

Calculation:

The derivative of D(t) is D(t), which is obtained as follows:

D(t)=ddt(1+16t2(4t)3) =ddt(1+16t264t3)=ddt(164t3+16t264t3)=ddt(164t3+14t)

Apply the sum rule as shown in equation (3)

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