document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #592456 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is really a beginning calculus problem.
\n" ); document.write( "You need the value of the derivative with respect to $\"s\"$ of the function $\"V=s%5E3\"$ .
\n" ); document.write( "That derivative can ve represented as $\"dV%2Fds\"$ or as $\"%22V%27%22\"$ .
\n" ); document.write( "For any value of $\"x\"$ that derivative (as a function of $\"x\"$ ) is
\n" ); document.write( " $\"%22V%27%28x%29%22=3x%5E2\"$ ,
\n" ); document.write( "and for $\"x=6\"$ , its value is
\n" ); document.write( " $\"%22V%27%286%29%22=3%2A6%5E2=3%2A36=108\"$ .
\n" ); document.write( "
\n" ); document.write( "NOTE: The derivative of any power, is the exponent times the power with an exponent that is one unit less.
\n" ); document.write( "If $\"f%28x%29=x%5Ep\"$ , then $\"%22F%27%28x%29%22=p%2Ax%5E%28%28p-1%29%29\"$ \n" ); document.write( "

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