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Find f'(x) and f"(x) for the following:

{eq}f(x) = 2x^3 - 9x + 1 {/eq}

Question:

Find f'(x) and f"(x) for the following:

{eq}f(x) = 2x^3 - 9x + 1 {/eq}

Power Rule

One of the most important differentiation rules is the power rule. This rule applies when we have functions containing our variable to a numerical exponent, regardless of if that exponent is positive, negative, an integer, or a fraction. This rule states that {eq}\frac{d}{dx} x^n = nx^{n-1} {/eq}.

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In order to find both of the derivatives of these functions, we'll need to apply the Power Rule. In conjunction with this rule, we can remember that...

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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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