   Chapter 11.5, Problem 50E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] s ( x ) = e 4 x − 1 x 3 − 1

To determine

To calculate: The derivative of the function s(x)=e4x1x31.

Explanation

Given information:

The provided function is s(x)=e4x1x31.

Formula used:

Quotient rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f'(x)g(x)f(x)g'(x)[g(x)]2 where g(x)0.

The derivative of e raised to a function is ddxeu=eududx.

Constant multiple rule of derivative of function f(x) is f(cx)=cf(x) where c is constant.

Calculation:

Consider the provided function,

s(x)=e4x1x31

Apply quotient rule of derivative,

s(x)=ddx(e4x1)(x31)e4x1ddx(x31)(x31)2

The derivative of e raised to a function is ddxeu=eududx.

Apply the above formula and take the derivative of (e4x1),

s(x)=e4x1ddx(4x1)(x31)e4x1(3x2)(x31)2

Apply constant multiple rule for the derivative of (

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