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Numerade Educator

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Problem 1 Easy Difficulty

If $ V $ is the volume of a cube with edge length $ x $ and the cube expands as time passes, find $ dV/dt $ in terms of $ dx/dt. $

Answer

$3 x^{2} \frac{d x}{d t}$

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Video Transcript

you know? Yeah. Were given a function V. We're told that he is the volume of a cube with eggs edge length X and the cube expands as time passes. Brass defines DVD t in terms of the exit. Well, you know, the volume of a cube with edge length X he simply execute. And therefore, if we treat this actually as a function of t so we have the F t is equal to x of t huge as a then taking the derivative with respect to t DVD T is equal to using chain rule three times X squared times, dx, DT. And so we've written DVT in terms of DX DT, yeah.