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The Power Rule of Derivatives



Power Rule Formula

Play For any real number, n :
$ \frac{d}{dx} x^n = $
Power Rule Example

Examples of The Power Rule

Play $ \frac{d}{dx} x^5 = $ Power Rule Example

How do we deal with coefficients?

Play

$ \frac{d}{dx} 3x^8 = $
Power Rule Example
Play

$ \frac{d}{dx} - \sqrt{2}x^7 = $
Power Rule Example

How do we deal with Rational Exponents?

Play

$ \frac{d}{dx} \sqrt[3]{x^2} = $
Power Rule Example

How about negative exponents?

Play

$ \frac{d}{dx} x^{-4} = $
Power Rule Example

Lastly, what about irrational numbers?

Play

$ \frac{d}{dx} x^{\sqrt{2}} = $
Power Rule Example

Practice Problems

Apply the power rule to find the derivative of the expressions below.


Problem 1)


$ \frac{d}{dx} x^7 $
Answer
Problem 2)


$ \frac{d}{dx} 3x^7 $
Answer
Problem 3)


$ \frac{d}{dx} \sqrt{2}x^{12} $
Answer
Problem 4)


$ \frac{d}{dx} \sqrt{5}x^{-6} $
Answer
Problem 5)


$ \frac{d}{dx} \frac{2}{3x^8} $
Answer
Problem 6)


$ \frac{d}{dx} \sqrt[5]{x^2} $
Answer