# Problem of the Week

## Updated at Oct 10, 2016 9:09 AM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of $$\csc{x}-\tan{x}$$?

Check out the solution below!

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

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