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 t7+et{t}^{7}+{e}^{t}?

Here are the steps:



ddtt7+et\frac{d}{dt} {t}^{7}+{e}^{t}

1
Use Sum Rule: ddxf(x)+g(x)=(ddxf(x))+(ddxg(x))\frac{d}{dx} f(x)+g(x)=(\frac{d}{dx} f(x))+(\frac{d}{dx} g(x)).
(ddtt7)+(ddtet)(\frac{d}{dt} {t}^{7})+(\frac{d}{dt} {e}^{t})

2
Use Power Rule: ddxxn=nxn−1\frac{d}{dx} {x}^{n}=n{x}^{n-1}.
7t6+(ddtet)7{t}^{6}+(\frac{d}{dt} {e}^{t})

3
The derivative of ex{e}^{x} is ex{e}^{x}.
7t6+et7{t}^{6}+{e}^{t}

Done
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