# Problem of the Week

## Updated at Mar 31, 2014 4:53 PM

This week we have another calculus problem:

How can we solve for the derivative of $$\cot{x}-\tan{x}$$?

Let's start!

$\frac{d}{dx} \cot{x}-\tan{x}$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} \cot{x})-(\frac{d}{dx} \tan{x})$2 Use Trigonometric Differentiation: the derivative of $$\cot{x}$$ is $$-\csc^{2}x$$.$-\csc^{2}x-(\frac{d}{dx} \tan{x})$3 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.$-\csc^{2}x-\sec^{2}x$Done-csc(x)^2-sec(x)^2