# Problem of the Week

## Updated at Oct 26, 2015 2:18 PM

This week we have another calculus problem:

How can we find the derivative of $$4x\cot{x}$$?

Let's start!

$\frac{d}{dx} 4x\cot{x}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$4(\frac{d}{dx} x\cot{x})$2 Use Product Rule to find the derivative of $$x\cot{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$4((\frac{d}{dx} x)\cot{x}+x(\frac{d}{dx} \cot{x}))$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$4(\cot{x}+x(\frac{d}{dx} \cot{x}))$4 Use Trigonometric Differentiation: the derivative of $$\cot{x}$$ is $$-\csc^{2}x$$.$4(\cot{x}-x\csc^{2}x)$Done4*(cot(x)-x*csc(x)^2)