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 \(\tan{x}{e}^{x}\)?

Let's start!



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

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

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

3
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[{e}^{x}\sec^{2}x+\tan{x}{e}^{x}\]

Done
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