Problem of the Week

Updated at Aug 12, 2013 10:11 AM

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

How can we solve for the derivative of \({x}^{7}\cos{x}\)?

Here are the steps:



\[\frac{d}{dx} {x}^{7}\cos{x}\]

1
Use Product Rule to find the derivative of \({x}^{7}\cos{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} {x}^{7})\cos{x}+{x}^{7}(\frac{d}{dx} \cos{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[7{x}^{6}\cos{x}+{x}^{7}(\frac{d}{dx} \cos{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\cos{x}\) is \(-\sin{x}\).
\[7{x}^{6}\cos{x}-{x}^{7}\sin{x}\]

Done
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