   Chapter 3.1, Problem 6E

Chapter
Section
Textbook Problem

Differentiate the function. g ( x ) = 7 4 x 2 − 3 x + 12

To determine

To find: The derivative of the function g(x).

Explanation

Given:

The function, g(x)=74x23x+12.

Formula used:

Derivative of a Constant Function

If c is a constant function, then ddx(c)=0 (1)

The Constant Multiple Rule

If c is a constant and f(x) is a differentiable function, then the constant multiple rule is,

ddx[cf(x)]=cddxf(x) (2)

The Power Rule:

If n is any real number, then the power rule is,

ddx(xn)=nxn1 (3)

The Sum Rule:

If f(x) and g(x) are both differentiable, then the sum rule is,

ddx[f(x)+g(x)]=ddx(f(x))+ddx(g(x)) (4)

The Difference Rule:

If f(x) and g(x) are both differentiable, then the difference rule is,

ddx[f(x)g(x)]=ddx(f(x))ddx(g(x)) (5)

Calculation:

The derivative of g(x)=74x23x+12 is g(x) as follows,

g(x)=ddx(g(x)) =ddx(74x23x+12)

Apply the sum rule as shown in equation (4)

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