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 xln⁡xx\ln{x}?

Let's begin!



ddxxln⁡x\frac{d}{dx} x\ln{x}

1
Use Product Rule to find the derivative of xln⁡xx\ln{x}. The product rule states that (fg)′=f′g+fg′(fg)'=f'g+fg'.
(ddxx)ln⁡x+x(ddxln⁡x)(\frac{d}{dx} x)\ln{x}+x(\frac{d}{dx} \ln{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
ln⁡x+x(ddxln⁡x)\ln{x}+x(\frac{d}{dx} \ln{x})

3
The derivative of ln⁡x\ln{x} is 1x\frac{1}{x}.
ln⁡x+1\ln{x}+1

Done
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