I read some stuff about partial derivative. If I understood correctly, partial derivative is when you consider all other variables as constant and independent and total derivative is when you dont consider them constant, you consider the direct or indirect contribution of every variable.
But here I have those functions and I don't know how to deal with them :
$\epsilon = \frac{x-\mu}{\sigma}$
$f(x, \sigma, \mu) = log(\sigma) - (\frac{x - \mu}{\sigma})^{2}$
I want to calculate $\frac{\partial f}{\partial \sigma}$
Should I consider $(\frac{x - \mu}{\sigma})^{2}$ as a constant because its equal to epsilon, or not ? I am confused, if someone could explain to me