   Chapter 11.3, Problem 44E 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 = 3 x 2 − 9 x + 11 2 x + 4

To determine

To calculate: The derivative of function y=3x29x+112x+4.

Explanation

Given Information:

The function is y=3x29x+112x+4.

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.

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.

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 function, y=3x29x+112x+4

Apply quotient rule of derivative,

dydx=ddx(3x29x+11)(2x+4)(3x29x+11)ddx(2x+4)(2x+4)2

Apply sum and difference rule of derivative,

dydx=[ddx(3x2)ddx(9x)+ddx(11)](2x+4)(3x29x+11)[ddx(2x)+ddx(4)

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