I have the following equation:
$$f\left(b,\ c,\ d\right)\ =\ 1\ -\ \left(\frac{\max\left(b,\ 0.00001\right)}{c}\right)^d$$
where $b$, $c$ and $d$ are variables (they can vary): $b\ \ge\ 0$, $c\ \ge\ 1$, and $d\ >\ 0$
I want to know, in what cases this function is non-differentiable? In other words, what combinations of $b$, $c$, and $d$ make this function's derivative undefined?
Background (in case it is necessary): I have a neural networks (NN) model that predicts the variables $b$, $c$, and $d$. And then, these variables are used within the equation above. Let's say $a\ =\ f\left(b,\ c,\ d\right)$ when $b$, $c$, and $d$ are predicted. And then loss between $a$ (prediction) and $\widehat{a}$ (target) is computed:
$$loss\ =\ f_{loss}\left(a,\ \widehat{a}\right)$$
Using back-propagation, I want to minimise the loss. But due to the above function being non-differentiable at some combinations of the variables, I cannot train the model. I want to know what values of $b$, $c$, and $d$ make this function non-differentiable so that I can restrict the values.