# Problem of the Week

## Updated at Nov 13, 2017 2:42 PM

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

Below is the solution.

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

 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 Use Trigonometric Differentiation: 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)