# Problem of the Week

## Updated at Sep 19, 2016 8:54 AM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of $${x}^{7}\sin{x}$$?

Check out the solution below!

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

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