Help for math test: For V=Pi*R^2*H, find total differation for dV

[Sleverine]

Heya everyone,

I'm studying for my math test but i got stuck on the implicite function part. I was wondering if i solved this one alright:

Given: V=Pi*R^2*H

A) Give the total differation for dV

B) What is dH/dR knowing its an implicite function with V constant.

My answers:

A) dV/dR=2Pi*R*H
dV/dH=Pi*R^2

This would make the answer:
dV=2Pi*R*H*dR+Pi*R^2*dH
Is this one correct?

B) This is were i get stuck as it has been a while since i did this.

I figured i could change it into:

0=(Pi*R^2*H) / V

I hope some 1 is able to help me
Thanks for reading

 

[Ishuda]

Heya everyone,

I'm studying for my math test but i got stuck on the implicite function part. I was wondering if i solved this one alright:

Given: V=Pi*R^2*H

A) Give the total differation for dV

B) What is dH/dR knowing its an implicite function with V constant.

My answers:

A) dV/dR=2Pi*R*H
dV/dH=Pi*R^2

This would make the answer:
dV=2Pi*R*H*dR+Pi*R^2*dH
Is this one correct?

B) This is were i get stuck as it has been a while since i did this.

I figured i could change it into:

0=(Pi*R^2*H) / V <========wrong

I hope some 1 is able to help me
Thanks for reading

Assuming V is not zero, it should be
1=(Pi*R^2*H) / V
If you then take the derivative wrt x say, you would have, using the product rule
0 = (2 PI R dR/dx + Pi R^2 dH/dx)/V - ((Pi*R^2*H) dV/dx)/V^2
Rearranging, this becomes
0 = (2 PI R dR/dx + Pi R^2 dH/dx)/V - [(Pi*R^2*H)/V] dV/dx)/V
and, using our initial equation and multiplying through by V and dx, we have
0 = 2 PI R dR + Pi R^2 dH - dV
or
dV = 2 PI R dR + Pi R^2 dH
which is what you have for (A).