# Problem of the Week

## Updated at Aug 30, 2021 3:31 PM

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

How would you differentiate $$\cos{z}+\csc{z}$$?

Here are the steps:

$\frac{d}{dz} \cos{z}+\csc{z}$

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