   Chapter 11.3, Problem 39E 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 = ( 5.3 x − 1 ) ( 1 − x 2.1 ) ( x − 2.3 − 3.4 )

To determine

To calculate: The derivative of function y=(5.3x1)(1x2.1)(x2.33.4).

Explanation

Given Information:

The function is y=(5.3x1)(1x2.1)(x2.33.4).

Formula used:

Product rule of derivative of differentiable functions f, g and h is,

(fgh)'=f'gh+fg'h+fgh'

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

Derivative of a constant is 0.

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=(5.3x1)(1x2.1)(x2.33.4).

Apply product rule of derivative,

dydx=ddx(5.3x1)(1x2.1)(x2.33.4)+(5.3x1)ddx(1x2.1)(x2.33.4)+(5.3x1)(1x2.1)ddx(x2.33.4)

Apply difference rule of derivative,

dydx=[ddx(5.3x)ddx(1)](1x2.1)(x2.33.4)+(5.3x1)[ddx(1)ddx(x2.1)](x2

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