Problem of the Week

Updated at Feb 19, 2024 8:03 AM

This week we have another calculus problem:

How can we find the derivative of \({e}^{q}+\tan{q}\)?

Let's start!



\[\frac{d}{dq} {e}^{q}+\tan{q}\]

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

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

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

Done
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