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 \(\cos{x}\)
\[5{x}^{4}\sin{x}+{x}^{5}\cos{x}\]

Done