Problem of the Week

Updated at Aug 22, 2016 2:02 PM

How can we solve for the derivative of x8ex{x}^{8}{e}^{x}?

Below is the solution.



ddxx8ex\frac{d}{dx} {x}^{8}{e}^{x}

1
Use Product Rule to find the derivative of x8ex{x}^{8}{e}^{x}. The product rule states that (fg)′=f′g+fg′(fg)'=f'g+fg'.
(ddxx8)ex+x8(ddxex)(\frac{d}{dx} {x}^{8}){e}^{x}+{x}^{8}(\frac{d}{dx} {e}^{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
8x7ex+x8(ddxex)8{x}^{7}{e}^{x}+{x}^{8}(\frac{d}{dx} {e}^{x})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
8x7ex+x8ex8{x}^{7}{e}^{x}+{x}^{8}{e}^{x}

Done
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