# Problem of the Week

## Updated at Jul 27, 2015 2:12 PM

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

Below is the solution.

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

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dx} x)+(\frac{d}{dx} \csc{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$1+(\frac{d}{dx} \csc{x})$3 Use Trigonometric Differentiation: the derivative of $$\csc{x}$$ is $$-\csc{x}\cot{x}$$.$1-\csc{x}\cot{x}$Done1-csc(x)*cot(x)