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
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