   Chapter 11.4, Problem 40E 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 1-50, calculate the derivate of the function. [HINT: See Example 1.] g ( z ) = ( z 2 1 + z ) 2

To determine

To calculate: The derivative of the function g(z)=(z21+z)2.

Explanation

Given Information:

The provided function is g(z)=(z21+z)2.

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.

A derivative of a function f(x)=(u)n using chain rule is f'(x)=ddx(un)=nun1dudx, where u is the function of x.

Sum rule of the derivative is ddx[f(x)+g(x)]=ddxf(x)+ddxg(x).

Calculation:

Consider the function,

g(z)=(z21+z)2

Apply chain rule,

h(z)=2(z21+z)21ddz(z21+z)=2(z21+z)ddz(z21+z)

Apply the quotient rule to the function (z21+z),

g(z)=2(z21+z)[(ddz(z2))(1+z)(z2)(ddz(1+z)

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