If {eq}f(x) = -9x + 6 {/eq}, find {eq}f'(x) {/eq}.

Find {eq}f'(3) {/eq}.

Find {eq}f'(0) {/eq}.

Find {eq}f'(-1) {/eq}.


If {eq}f(x) = -9x + 6 {/eq}, find {eq}f'(x) {/eq}.

Find {eq}f'(3) {/eq}.

Find {eq}f'(0) {/eq}.

Find {eq}f'(-1) {/eq}.

Power Rule:

The power rule of differentiation is a differentiation rule that applies to any power function of the form {eq}\displaystyle x^n {/eq}. Basically, the power rule states that the derivative of a term like this is:

{eq}\displaystyle \frac{d}{dx} \left[x^n \right] = nx^{n-1} {/eq}

This rule is valid for any n as long as it isn't zero. In that case, then the power function essentially becomes a constant, in which the derivative is zero.

Answer and Explanation: 1

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  • {eq}\displaystyle f(x)= -9x + 6 {/eq}

Let us take the derivative of this function. We use the power rule:

{eq}\displaystyle \frac{d}{dx}...

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Learn more about this topic:

Power Rule for Derivatives: Examples & Explanation


Chapter 19 / Lesson 18

In this lesson, learn the power rule for the derivative of exponents. Moreover, learn to understand how to apply the power rule of derivatives for various cases including negative powers.

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