Question

the radius of a right cylinder is increasing at the rate of 9in./sec, while the height is decreasing at the rate of 7in./sec. at what rate is the volume of the cylinder changing when the radius is 15in. and the height is 18in.?

Answer 1

Does this look better... maybe? >.<

Answer 2

Volume of a cylinder is,\[\Large\rm V=\pi r^2 h\]Let's differentiate our volume function with respect to `time`.
So we'll be getting a bunch of prime terms popping out, yes?

Answer 3

\[\Large\rm V'=\pi(r^2)'h+\pi r^2(h)'\]Product rule, yes?

Answer 4

Leading to,\[\Large\rm V'=2\pi rhr'+\pi r^2h'\]Any confusion there on taking the derivative?