   Chapter 11.3, Problem 34E 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 = ( 2 x 0.5 − x 2 ) 2

To determine

To calculate: The derivative of function y=(2x0.5x2)2.

Explanation

Given Information:

The function is y=(2x0.5x2)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.

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 function, y=(2x0.5x2)2.

Rewrite the function as the product of two binomials,

y=(2x0.5x2)2=(2x0.5x2)(2x0.5x2)

Apply product rule of derivative,

dydx=ddx(2x0.5x2)(2x0.5x2)+(2x0.5x2)ddx(2x0

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