# Problem of the Week

## Updated at Aug 1, 2016 3:10 PM

This week's problem comes from the calculus category.

How would you differentiate $${x}^{9}\sec{x}$$?

Let's begin!

$\frac{d}{dx} {x}^{9}\sec{x}$

 1 Use Product Rule to find the derivative of $${x}^{9}\sec{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} {x}^{9})\sec{x}+{x}^{9}(\frac{d}{dx} \sec{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$9{x}^{8}\sec{x}+{x}^{9}(\frac{d}{dx} \sec{x})$3 Use Trigonometric Differentiation: the derivative of $$\sec{x}$$ is $$\sec{x}\tan{x}$$.$9{x}^{8}\sec{x}+{x}^{9}\sec{x}\tan{x}$Done9*x^8*sec(x)+x^9*sec(x)*tan(x)