Differentiate f(x)=(3x+4)^2. a. f'(x)=6(3x+4)^2 b.f'(x)=2(3x+4) c. f'(x)=6(3x+4) d. f'(x)=3(3x+4)

Question:

Differentiate {eq}f(x)=(3x+4)^2 {/eq}.

a. {eq}f'(x)=6(3x+4)^2 {/eq}

b. {eq}f'(x)=2(3x+4) {/eq}

c. {eq}f'(x)=6(3x+4) {/eq}

d. {eq}f'(x)=3(3x+4) {/eq}

Differentiation:

There are several rules to determine the derivative of a function. The basic rules are the product rule, quotient rule, and the chain rule. We must not forget that when a function can be expressed in terms of another function, we must apply the chain rule.

Answer and Explanation:

For this question, we must apply the chain rule to properly differentiate the function. If we let {eq}g(x) = 3x+4 {/eq} so {eq}g'(x) = 3 {/eq}, we...

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Using the Chain Rule to Differentiate Complex Functions

from Math 104: Calculus

Chapter 9 / Lesson 6
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