Problem of the Week

Updated at Jul 21, 2014 2:02 PM

How can we solve for the derivative of \({x}^{8}\tan{x}\)?

Below is the solution.



\[\frac{d}{dx} {x}^{8}\tan{x}\]

1
Use Product Rule to find the derivative of \({x}^{8}\tan{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} {x}^{8})\tan{x}+{x}^{8}(\frac{d}{dx} \tan{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[8{x}^{7}\tan{x}+{x}^{8}(\frac{d}{dx} \tan{x})\]

3
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[8{x}^{7}\tan{x}+{x}^{8}\sec^{2}x\]

Done
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