Chapter 2.3, Problem 30E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding a Derivative In Exercises 29-40, Find the derivative of the algebraic function. f ( x ) = x 2 + 5 x + 6 x 2 − 4

To determine

To calculate: The derivative of the algebraic function f(x)=x2+5x+6x24.

Explanation

Given:

The function is f(x)=x2+5x+6x2âˆ’4.

Formula used:

The Quotient Rule states that,

(vg)â€²=gvâ€²âˆ’vgâ€²g2

The power rule of differentiation states that

ddxxn=nxnâˆ’1

Calculation:

Consider the function,

f(x)=x2+5x+6x2âˆ’4

Recall the quotient rule,

(vg)â€²=gvâ€²âˆ’vgâ€²g2

Let v(x)=x2+5x+6 and g(x)=x2âˆ’4,

Substitute the value of v and g in the quotient rule and differentiate the function with respect to x,

fâ€²(x)=(x2âˆ’4)(ddx(x2+5x+6))âˆ’(ddx(x2âˆ’4))(x2+5x+6)(x2âˆ’4)2=(x2âˆ’4)(2x+5)âˆ’2x(

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