# Problem of the Week

## Updated at May 22, 2017 5:29 PM

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

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

Check out the solution below!

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

 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} \cos{x})$2 Use Trigonometric Differentiation: the derivative of $$\cot{x}$$ is $$-\csc^{2}x$$.$-\csc^{2}x-(\frac{d}{dx} \cos{x})$3 Use Trigonometric Differentiation: the derivative of $$\cos{x}$$ is $$-\sin{x}$$.$\sin{x}-\csc^{2}x$Donesin(x)-csc(x)^2