   Chapter 9.6, Problem 14E ### 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. g ( t ) = 1 4 t 3 + 1

To determine

To calculate: The derivative of the function g(t)=14t3+1.

Explanation

Given Information:

The provided function is g(t)=14t3+1.

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.

If any nonzero real number a has a negative integer n as its exponent then an=1an.

Calculation:

Consider the function,

g(t)=14t3+1

Rewrite the function as,

g(t)=(4t3+1)1

Consider (4t3+1) to be u,

g(t)=u1

Differentiate both sides with respect to t,

g(t)=ddt(u1)

Use the power rule,

g(t)=1u11d<

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