Problem of the Week

Updated at Aug 22, 2016 2:02 PM

How can we solve for the derivative of \({x}^{8}{e}^{x}\)?

Below is the solution.



\[\frac{d}{dx} {x}^{8}{e}^{x}\]

1
Use Product Rule to find the derivative of \({x}^{8}{e}^{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} {x}^{8}){e}^{x}+{x}^{8}(\frac{d}{dx} {e}^{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[8{x}^{7}{e}^{x}+{x}^{8}(\frac{d}{dx} {e}^{x})\]

3
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[8{x}^{7}{e}^{x}+{x}^{8}{e}^{x}\]

Done
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