# Problem of the Week

## Updated at Oct 25, 2021 5:35 PM

This week's problem comes from the calculus category.

How can we solve for the derivative of $$\csc{y}+6y$$?

Let's begin!

$\frac{d}{dy} \csc{y}+6y$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dy} \csc{y})+(\frac{d}{dy} 6y)$2 Use Trigonometric Differentiation: the derivative of $$\csc{x}$$ is $$-\csc{x}\cot{x}$$.$-\csc{y}\cot{y}+(\frac{d}{dy} 6y)$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$-\csc{y}\cot{y}+6$Done-csc(y)*cot(y)+6