Problem of the Week

Updated at Feb 17, 2014 3:51 PM

For this week we've brought you this calculus problem.

How can we find the derivative of \(\tan^{3}x\)?

Here are the steps:



\[\frac{d}{dx} \tan^{3}x\]

1
Use Chain Rule on \(\frac{d}{dx} \tan^{3}x\). Let \(u=\tan{x}\). Use Power Rule: \(\frac{d}{du} {u}^{n}=n{u}^{n-1}\).
\[3\tan^{2}x(\frac{d}{dx} \tan{x})\]

2
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[3\tan^{2}x\sec^{2}x\]

Done
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