Problem of the Week

Updated at Mar 28, 2016 3:14 PM

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

How can we solve for the derivative of \({x}^{3}\tan{x}\)?

Check out the solution below!



\[\frac{d}{dx} {x}^{3}\tan{x}\]

1
Use Product Rule to find the derivative of \({x}^{3}\tan{x}\). The product rule states that \((fg)'=f'g+fg'\).
\[(\frac{d}{dx} {x}^{3})\tan{x}+{x}^{3}(\frac{d}{dx} \tan{x})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[3{x}^{2}\tan{x}+{x}^{3}(\frac{d}{dx} \tan{x})\]

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

Done
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