Problem of the Week

Updated at Jun 20, 2022 1:28 PM

This week we have another calculus problem:

How would you differentiate \({e}^{t}+{t}^{2}\)?

Let's start!



\[\frac{d}{dt} {e}^{t}+{t}^{2}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dt} {e}^{t})+(\frac{d}{dt} {t}^{2})\]

2
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[{e}^{t}+(\frac{d}{dt} {t}^{2})\]

3
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[{e}^{t}+2t\]

Done
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