Partial Differentials of two functions with 2 variables each

[CorvusCorax]

From the two equations given below, find ∂s/∂V (holding h constant) and ∂h/∂V (holding r constant
V = π*r^2*h, S = 2π*r*h + 2*π*r^2
Not entirely sure where to start...

 

[tiny-tim]

Welcome to PF!

Hi CorvusCorax! Welcome to PF!

… find ∂s/∂V (holding h constant)
…
V = π*r^2*h, S = 2π*r*h + 2*π*r^2

What is S as a function of V and h ?

 

[CorvusCorax]

Hi CorvusCorax! Welcome to PF!


What is S as a function of V and h ?

Thanks. Been a lurker for years on several sites, decided it is probably time to join up for my own questions.

I'd say the first part of S, 2*pi*r*h, is just V'. I guess I could say 2*pi*r^2 is equivalent to 2*(V/h). So at that point just take the partial w/respect to V?

 

[tiny-tim]

I guess I could say 2*pi*r^2 is equivalent to 2*(V/h).

Yes.

I'd say the first part of S, 2*pi*r*h, is just V'.

No, that's not an expression in V and h.

(and now I'm off to bed :zzz:)