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}.

Question:

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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Given:

  • {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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Power Rule for Derivatives: Examples & Explanation

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Chapter 19 / Lesson 18
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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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