# 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-sin(x)/cos(x)