# Problem of the Week

## Updated at Jan 11, 2021 10:20 AM

This week's problem comes from the calculus category.

How can we solve for the derivative of $$\tan{q}+5q$$?

Let's begin!

$\frac{d}{dq} \tan{q}+5q$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dq} \tan{q})+(\frac{d}{dq} 5q)$2 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.$\sec^{2}q+(\frac{d}{dq} 5q)$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$\sec^{2}q+5$Donesec(q)^2+5