# Problem of the Week

## Updated at Aug 29, 2022 11:16 AM

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

How would you differentiate $$\tan{y}+{y}^{7}$$?

Here are the steps:

$\frac{d}{dy} \tan{y}+{y}^{7}$

 1 Use Sum Rule: $$\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))$$.$(\frac{d}{dy} \tan{y})+(\frac{d}{dy} {y}^{7})$2 Use Trigonometric Differentiation: the derivative of $$\tan{x}$$ is $$\sec^{2}x$$.$\sec^{2}y+(\frac{d}{dy} {y}^{7})$3 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$\sec^{2}y+7{y}^{6}$Donesec(y)^2+7*y^6