   Chapter 9.6, Problem 9E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Differentiate the functions in Problems 3-20. s ( t ) = 5 t − 3 ( 2 t 4 + 7 ) 3

To determine

To calculate: The derivative of the function s(t)=5t3(2t4+7)3.

Explanation

Given Information:

The provided function is s(t)=5t3(2t4+7)3.

Formula used:

Power rule for a real number n is such that, if y=un then dydx=nun1dudx, where u is a differentiable function of x.

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Calculation:

Consider the function,

s(t)=5t3(2t4+7)3

Consider (2t4+7) to be u,

s(t)=5t3u3

Differentiate both sides with respect to t,

s(t)=ddt(5t3u3)=ddt(5t)ddt(3u3)=5ddt(t)3ddt(u3)

Use the power rule,

s(

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