Problem of the Week

Updated at Mar 19, 2018 5:22 PM

How would you differentiate \(\sec{x}{e}^{x}\)?

Below is the solution.



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

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

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

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

Done
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