Problem of the Week

Updated at Nov 11, 2013 9:46 AM

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

How would you differentiate \(\sec^{3}x\)?

Here are the steps:



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

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

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

Done
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