   Chapter 9.7, Problem 20E ### 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

# Find the derivatives of the functions in Problems 1-32. Simplify and express the answer using positive exponents only. s = [ ( 4 − t 2 ) ( t 2 + 5 t ) ] 4

To determine

To calculate: The simplified form of the derivative of function s=[(4t2)(t2+5t)]4.

Explanation

Given Information:

The provided function is s=[(4t2)(t2+5t)]4.

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.

Product rule for function f(x)=u(x)v(x), where u and v are differentiable functions of x, then f(x)=u(x)v(x)+v(x)u(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=[(4t2)(t2+5t)]4

Consider (4t2)(t2+5t) to be u,

s=u4

Differentiate both sides with respect to t,

s=ddt(u4)

Use the power rule,

s=4u41dudt=4u3dudt

Substitute (4t2)(t2+5t) for u,

s=4(4t2)(t2+5t)3ddt[(4

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