Assume to have a quantity A which is calculated from the formula $A=\frac{dB}{dC}$. dC can be written as dC=dEdF so $A=\frac{dB}{dEdF}$. I assume that the differential of A is also $dA=\frac{dB}{dEdF}$. I would like to take the derivative with respect to z. So, I have $\frac{dA}{dz}=\frac{d}{dz}(\frac{dB}{dEdF})$. In which cases can I write this relation as $\frac{dA}{dz}=\frac{dB}{dEdFdz}$ ? I want this form because in my case $\frac{dB}{dzdF}$ forms a quantity of interest for me (name it G) and thus $\frac{dA}{dz}=\frac{dG}{dB}$. The questions is that under what circumstances can I change the series of differentation?
Another possible writting is $\frac{dA}{dz}=\frac{d^2B}{dEdFdz}$. Any further references will be appreciated. Thank you