differentials related rates.

[mammothrob]

So I have a frustum of a right circular cone. The radii and the height are changing at particular rates dr/dt dR/dt dh/dt which I have values for.

I need to find out the rate in which the Volume (dV/dt) is changing when the radii and height are at a specific value.

So V=(1/3)*pi*h (r^2 + rR + R^2)

In this section of my math book Chain rules for differentials and partial differentiation are the topic.

My question is... why do I need a chain rule for this problem? can't I just find the differential dV? I ahh just dont see where the chain rule comes in here.

This is what I see....


& = notation for partial derivative (I need to learn latex)

dV = (&V/&r)(dr/dt) + (&V/&R)(dR/dt) + (&V/&h)(dh/dt)

am I just missing something right in front of me....?

 

[mammothrob]

i see whats going on here... I already have the rates so I dont need to find the derivatives for other functions, since they are fixed rates. If the rates were changing though I would need the functions that produce them. Ha. Haha.