Problem of the Week

Updated at Feb 16, 2015 3:42 PM

How can we find the derivative of \({x}^{9}\ln{x}\)?

Below is the solution.



\[\frac{d}{dx} {x}^{9}\ln{x}\]

1
Use Product Rule to find the derivative of \({x}^{9}\ln{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} {x}^{9})\ln{x}+{x}^{9}(\frac{d}{dx} \ln{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[9{x}^{8}\ln{x}+{x}^{9}(\frac{d}{dx} \ln{x})\]

3
The derivative of \(\ln{x}\) is \(\frac{1}{x}\).
\[9{x}^{8}\ln{x}+{x}^{8}\]

Done
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