Problem of the Week

Updated at Oct 14, 2019 4:41 PM

For this week we've brought you this calculus problem.

How can we solve for the derivative of \({t}^{7}+{e}^{t}\)?

Here are the steps:



\[\frac{d}{dt} {t}^{7}+{e}^{t}\]

1
Use Sum Rule: \(\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x))\).
\[(\frac{d}{dt} {t}^{7})+(\frac{d}{dt} {e}^{t})\]

2
Use Power Rule: \(\frac{d}{dx} {x}^{n}=n{x}^{n-1}\).
\[7{t}^{6}+(\frac{d}{dt} {e}^{t})\]

3
The derivative of \({e}^{x}\) is \({e}^{x}\).
\[7{t}^{6}+{e}^{t}\]

Done
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