# PDE constrained to a curve

1. ### Sunfire

221
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?

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3. ### 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}##

4. ### Sunfire

221
Yes, thank you, this makes a lot of sense. The chain rule for partial derivatives.