Can I Modify a PDE Expression If It's Constrained to a Curve?

[Sunfire]

Hello folks,

If we have the expression, say

\frac{∂f}{∂r}+\frac{∂f}{∂θ}, am I allowed to change it to

\frac{df}{dr}+\frac{df}{dr}\frac{dr}{dθ},

if "f" is constrained to the curve r=r(θ).

My reasoning is that since the curve equation is known, then f does not really depend on the angle θ, but only on r (and r is a function of the angle, kind of a compound function).

Does this make sense?

 

[Khashishi]

This seems right conceptually, but notationally, some of those should be partial derivatives.
$\frac{\partial f}{\partial r} + \frac{\partial f}{\partial r} \frac{dr}{d\theta} = \frac{df}{dr}$

 

[Sunfire]

Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.