# Problem of the Week

## Updated at Jan 18, 2016 9:00 AM

This week's problem comes from the calculus category.

How can we find the derivative of $$\sin{x}+\cot{x}$$?

Let's begin!

$\frac{d}{dx} \sin{x}+\cot{x}$

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