Problem of the Week

Updated at Jul 11, 2016 9:18 AM

This week we have another calculus problem:

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

Let's start!

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

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