# Problem of the Week

## Updated at Mar 27, 2017 3:37 PM

How would you differentiate $$\cos{x}-\cot{x}$$?

Below is the solution.

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

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