Question

What is the derivative of `v=1/3pir^2h`?

Answer 1

`(dv)/dt=(2pirh)/3((dr)/dt)+(pir^2)/3((dh)/dt)`

Explanation:

if you're doing related rates, you're probably differentiating with respect to `t` or time:
`d/dt(v)=d/dt(pi/3r^2h)`
`(dv)/dt=pi/3d/dt(r^2h)`
`(dv)/dt=pi/3(d/dt(r^2)h+d/dt(h)r^2)`
`(dv)/dt=pi/3(2rd/dt(r)h+(dh)/dtr^2)`
`(dv)/dt=pi/3(2r((dr)/dt)h+((dh)/dt)r^2)`
`(dv)/dt=(2pirh)/3((dr)/dt)+(pir^2)/3((dh)/dt)`