Chapter 9, Problem 66RE

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# 66.  Find d s d t  if  s = t ( 3 t + 1 ) .

To determine

To calculate: The value of dsdt for the function s=t(3t+1).

Explanation

Given Information:

The provided function is s=t(3t+1).

Formula used:

Quotient rule for function f(x)=u(x)v(x), where u and v are differentiable functions of x, then fâ€²(x)=v(x)â‹…uâ€²(x)âˆ’u(x)â‹…vâ€²(x)[v(x)]2.

Power of x rule for function f(x)=xn is fâ€²(x)=nxnâˆ’1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

Calculation:

Consider the function, s=t(3t+1)

Differentiate both sides with respect to t,

dsdt=ddt(t(3t+1))

Use the quotient rule,

dsdt=(3t+1)ddt(t1/2)âˆ’t1/2ddt(3t+1)(3t+1)2=(3t+1)ddt(t1/2)âˆ’t1/2

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