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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. $

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

02:37

Alex L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

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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.

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