Problem of the Week

Updated at May 1, 2023 1:43 PM

This week we have another calculus problem:

How would you differentiate \({e}^{m}+\tan{m}\)?

Let's start!



\[\frac{d}{dm} {e}^{m}+\tan{m}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dm} {e}^{m})+(\frac{d}{dm} \tan{m})\]

2
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[{e}^{m}+(\frac{d}{dm} \tan{m})\]

3
Use Trigonometric Differentiation: the derivative of \(\tan{x}\) is \(\sec^{2}x\).
\[{e}^{m}+\sec^{2}m\]

Done
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