Problem of the Week

Updated at Feb 3, 2014 2:01 PM

For this week we've brought you this calculus problem.

How would you differentiate xcos⁡xx\cos{x}?

Here are the steps:



ddxxcos⁡x\frac{d}{dx} x\cos{x}

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

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

3
Use Trigonometric Differentiation: the derivative of cos⁡x\cos{x} is −sin⁡x-\sin{x}.
cos⁡x−xsin⁡x\cos{x}-x\sin{x}

Done
Cymath foriOSAndroid