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 \(x\cos{x}\)?

Here are the steps:



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

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

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

3
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[\cos{x}-x\sin{x}\]

Done
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