# Problem of the Week

## Updated at Aug 12, 2013 10:11 AM

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

How can we solve for the derivative of $${x}^{7}\cos{x}$$?

Here are the steps:

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

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