# Problem of the Week

## Updated at Mar 2, 2015 9:46 AM

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

How would you differentiate $$8x\cot{x}$$?

Here are the steps:

$\frac{d}{dx} 8x\cot{x}$

 1 Use Constant Factor Rule: $$\frac{d}{dx} cf(x)=c(\frac{d}{dx} f(x))$$.$8(\frac{d}{dx} x\cot{x})$2 Use Product Rule to find the derivative of $$x\cot{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$8((\frac{d}{dx} x)\cot{x}+x(\frac{d}{dx} \cot{x}))$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$8(\cot{x}+x(\frac{d}{dx} \cot{x}))$4 Use Trigonometric Differentiation: the derivative of $$\cot{x}$$ is $$-\csc^{2}x$$.$8(\cot{x}-x\csc^{2}x)$Done8*(cot(x)-x*csc(x)^2)