Applications of Partial Derivatives and chain rule

[mit_hacker]

Homework Statement

The lengths a,b,c of a rectangle are changing with time. At the instant in question, a=1m, b=2m, c=3m and da/dt = db/dt = 1m/sec, and dc/dt = -3m/sec. At what rate is the box's volume changing at this instant?

Homework Equations

Chain rule for partial derivatives.

The Attempt at a Solution

∂V/∂t=(bc)(da/dt)+(ac)(db/dt)+(ab)(dc/dt)

Substituting the values gives 3m^3/s. Am I right?
Thanks for helping me out. The answer is not given in the book.

 

[EnumaElish]

The equation is correct.

 

[mit_hacker]

Thanks!

Hey! Thanks a ton for the re-assurances! Makes me feel more confident about myself.