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 x3tan⁡x{x}^{3}\tan{x}?

Check out the solution below!



ddxx3tan⁡x\frac{d}{dx} {x}^{3}\tan{x}

1
Use Product Rule to find the derivative of x3tan⁡x{x}^{3}\tan{x}. The product rule states that (fg)′=f′g+fg′(fg)'=f'g+fg'.
(ddxx3)tan⁡x+x3(ddxtan⁡x)(\frac{d}{dx} {x}^{3})\tan{x}+{x}^{3}(\frac{d}{dx} \tan{x})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
3x2tan⁡x+x3(ddxtan⁡x)3{x}^{2}\tan{x}+{x}^{3}(\frac{d}{dx} \tan{x})

3
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
3x2tan⁡x+x3sec⁡2x3{x}^{2}\tan{x}+{x}^{3}\sec^{2}x

Done
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