Problem of the Week

Updated at Oct 28, 2024 4:43 PM

This week we have another calculus problem:

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

Let's start!



\[\frac{d}{du} \sec{u}+{e}^{u}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{du} \sec{u})+(\frac{d}{du} {e}^{u})\]

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

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

Done
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