Jan 142016

Electricity warning signIf you’ve got the word “power” in your name, you’d better believe expectations are going to be sky high for what you can do. The Power Rule in calculus brings it and then some.

The Power Rule, probably the most used rule when differentiating, gives us a drop dead simple way to differentiate polynomials. Specifically it says for that any polynomial term x raised to the power n with coefficient a:

(1)   \begin{equation*} \frac{d}{dx}ax^n = nax^{n-1}, \qquad n \neq 0 \end{equation*}

Apply this to every term in your polynomial, and you’ve got its derivative! Easy peasy. Let’s prove it.

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