Problem of the Week

Updated at Jul 24, 2017 4:38 PM

This week we have another calculus problem:

How can we solve for the derivative of tan⁡xex\tan{x}{e}^{x}?

Let's start!



ddxtan⁡xex\frac{d}{dx} \tan{x}{e}^{x}

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

2
Use Trigonometric Differentiation: the derivative of tan⁡x\tan{x} is sec⁡2x\sec^{2}x.
exsec⁡2x+tan⁡x(ddxex){e}^{x}\sec^{2}x+\tan{x}(\frac{d}{dx} {e}^{x})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
exsec⁡2x+tan⁡xex{e}^{x}\sec^{2}x+\tan{x}{e}^{x}

Done
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