   Chapter 11.3, Problem 42E 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 29-56, calculate d y d x . You need not expand your answers. [HINT: See Example 1 and 2.] y = ( 4 x 2 − x ) ( x − 2 x 2 )

To determine

To calculate: The derivative of function y=(4x2x)(x2x2).

Explanation

Given Information:

The function is y=(4x2x)(x2x2).

Formula used:

Product 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)

Difference rule of derivative is ddx[f(x)g(x)]=ddx[f(x)]ddx[g(x)] where, f(x) and g(x) are any two differentiable functions.

Derivative of a constant is 0.

Derivative of function y=xn using power rule is dydx=nxn1.

Calculation:

Consider the function, y=(4x2x)(x2x2).

Convert to power form,

y=(4x2x12)(x122x2)

Apply product rule of derivative,

dydx=ddx(4x2x12)(x122x2)+(4x2x12)ddx(x122x2)

Apply difference rule of derivative,

dydx=[ddx(4x2)ddx(x12)](x122x2)+(4x2x12)[ddx

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