   Chapter 11.3, Problem 59E 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 57-62, compute the indicated derivatives. d d x [ ( x 3 + 2 x ) ( x 2 − x ) ] | x = 2

To determine

To calculate: The solution of the derivative ddx[(x3+2x)(x2x)] at x=2.

Explanation

Given Information:

The provided derivative is ddx[(x3+2x)(x2x)] and x=2.

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)

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

Constant multiple rule of derivative of function f(x) is ddx[cf(x)]=cddx[f(x)] where, c is constant.

Sum and 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.

Calculation:

Consider the provided derivative ddx[(x3+2x)(x2x)],

To find the derivative, apply product rule of derivative,

ddx[(x3+2x)(x2x)]=(x2x)ddx(x3+2x)+(x3+2x)ddx(x2x)

Now, apply sum and difference rule of derivative,

ddx[(x3+2x)(x2x)]=(x2x)[ddx(x3)+2ddx(x)]+(x3+2x)[ddx(x2)

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