Problem of the Week

Updated at Mar 17, 2014 10:11 AM

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

How can we solve for the derivative of \(\ln{(\cos{x})}\)?

Here are the steps:



\[\frac{d}{dx} \ln{(\cos{x})}\]

1
Use Chain Rule on \(\frac{d}{dx} \ln{(\cos{x})}\). Let \(u=\cos{x}\). The derivative of \(\ln{u}\) is \(\frac{1}{u}\).
\[\frac{1}{\cos{x}}(\frac{d}{dx} \cos{x})\]

2
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[-\frac{\sin{x}}{\cos{x}}\]

Done
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