Differentiate two variables functions

[chimay]

Hi,
I am dealing with an equality of the form:
$$f(x)=g(y,z)$$
and I need to compute $dx$.
Is the following relation correct?
$$dx={(\frac{\partial f}{\partial x})}^{-1}( \frac{\partial g}{\partial y}dy + \frac{\partial g}{\partial z}dz )$$

Thank you in advance.

 

[andrewkirk]

Yes, that's correct. Of course it breaks down at points where $\frac{\partial f}{\partial x}$ is zero, but maybe that's not in the domain of interest.

 

[chimay]

Thank you!