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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 $dx/dt.$

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

Derivatives

Differentiation

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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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.

Ohio State University

#### Topics

Derivatives

Differentiation

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp