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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. $

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02:37

Alex Lee

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Campbell University

Oregon State University

Harvey Mudd College

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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If V is the volume of a cu…

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1. If V is the volume of a…

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if v is the volume of a sp…

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The volume $V$ of a cube i…

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Volume Let $V$ be the volu…

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Volume The change in the v…

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The volume $V$ of a cube w…

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The change in the volume $…

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A cube is expanding with t…

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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