# Problem of the Week

## Updated at Jul 14, 2014 5:22 PM

How would you differentiate $${x}^{7}\sec{x}$$?

Below is the solution.

$\frac{d}{dx} {x}^{7}\sec{x}$

 1 Use Product Rule to find the derivative of $${x}^{7}\sec{x}$$. The product rule states that $$(fg)'=f'g+fg'$$.$(\frac{d}{dx} {x}^{7})\sec{x}+{x}^{7}(\frac{d}{dx} \sec{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$7{x}^{6}\sec{x}+{x}^{7}(\frac{d}{dx} \sec{x})$3 Use Trigonometric Differentiation: the derivative of $$\sec{x}$$ is $$\sec{x}\tan{x}$$.$7{x}^{6}\sec{x}+{x}^{7}\sec{x}\tan{x}$Done7*x^6*sec(x)+x^7*sec(x)*tan(x)