# Problem of the Week

Updated at Nov 13, 2017 2:42 PM

How can we find the derivative of $${x}^{5}\sin{x}$$?

Here's how to solve this problem.

$\frac{d}{dx} {x}^{5}\sin{x}$

 1 Use Product Rule to find the derivative of $${x}^{5}\sin{x}$$The product rule states that $$(fg)'=f'g+fg'$$$(\frac{d}{dx} {x}^{5})\sin{x}+{x}^{5}(\frac{d}{dx} \sin{x})$2 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$$5{x}^{4}\sin{x}+{x}^{5}(\frac{d}{dx} \sin{x})$3 The derivative of $$\sin{x}$$ is $$\cos{x}$$$5{x}^{4}\sin{x}+{x}^{5}\cos{x}$Done5*x^4*sin(x)+x^5*cos(x)