Hello folks, If we have the expression, say [itex]\frac{∂f}{∂r}[/itex]+[itex]\frac{∂f}{∂θ}[/itex], am I allowed to change it to [itex]\frac{df}{dr}[/itex]+[itex]\frac{df}{dr}[/itex][itex]\frac{dr}{dθ}[/itex], 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?
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}##