Problem of the Week

Updated at Jul 24, 2017 4:38 PM

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Jul 24, 2017

This week we have another calculus problem:

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

Let's start!

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

to find the derivative of \(\tan{x}{e}^{x}\)
The product rule states that \((fg)'=f'g+fg'\)

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

The derivative of \(\tan{x}\) is \(\sec^{2}x\)

\[{e}^{x}\sec^{2}x+\tan{x}(\frac{d}{dx} {e}^{x})\]

The derivative of \({e}^{x}\) is \({e}^{x}\)

\[{e}^{x}\sec^{2}x+\tan{x}{e}^{x}\]

Done