Problem of the Week

Updated at Dec 19, 2016 3:21 PM

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

How can we find the derivative of $$\csc{x}-{x}^{3}$$?

Here are the steps:

$\frac{d}{dx} \csc{x}-{x}^{3}$

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