SOLUTION: The volume of a cube with sides of length s is given by v=s^3. Find the rate of change of the volume with respect to s when s=6 centimeters. V'(6)=. cm^2

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Question 969626: The volume of a cube with sides of length s is given by v=s^3. Find the rate of change of the volume with respect to s when s=6 centimeters. V'(6)=. cm^2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
This is really a beginning calculus problem.
You need the value of the derivative with respect to s of the function V=s%5E3 .
That derivative can ve represented as dV%2Fds or as %22V%27%22 .
For any value of x that derivative (as a function of x ) is
%22V%27%28x%29%22=3x%5E2 ,
and for x=6 , its value is
%22V%27%286%29%22=3%2A6%5E2=3%2A36=108 .

NOTE: The derivative of any power, is the exponent times the power with an exponent that is one unit less.
If f%28x%29=x%5Ep , then %22F%27%28x%29%22=p%2Ax%5E%28%28p-1%29%29