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

1 Answer
May 25, 2018

#(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)#