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Numerade Educator

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Problem 24 Easy Difficulty

Find the derivative of the function.
$ f(t) = 2^{t^3} $

Answer

$2^{t^{3}} \ln 2 \cdot 3 t^{2}$

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Video Transcript

in this problem, we're finding the derivative of two to the power t cubed. So let me remind you that if you have an exponential function to to the X, it's derivative will be two to the X Times natural log tube. So if we apply the chain ruled to that and we have an exponential function to to the f of X. It's derivative will be two to the f of X times natural log two times the derivative of the inside, which would be f prime of X. So that's the situation we have going on here. So the derivative will be to to the t cubed times natural log to times the derivative of the inside function. So times the derivative of Tea Cube, which is three t squared