Problem of the Week

Updated at Feb 24, 2014 5:25 PM

This week's problem comes from the calculus category.

How would you differentiate \(x\ln{x}\)?

Let's begin!



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

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

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

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

Done
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