Problem of the Week

Updated at Sep 19, 2016 8:54 AM

To get more practice in calculus, we brought you this problem of the week:

How can we find the derivative of \({x}^{7}\sin{x}\)?

Check out the solution below!



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

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

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

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

Done
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