I have a probability function shown below, and I was wondering if it is possible to set the right side equal to 0, then take the derivative of the right side with respect to $P_j{_r}$ and find the global maximum. However, to do this the function should be continuous and I'm not sure if it is.
Assuming all variables other than $P_j{_r}$ are given constants, is this function continuous and is it possible to find the global maximum?
$$ Pr_j{_r}=\frac{y_j{_r}exp(\frac{x_j+x_r+b*log(P_j{_r})}{1-h})( \sum_{s=1}^R y_j{_s}exp(\frac{(x_j+x_s+b*log(P_j{_r}))}{1-h}))^-{^h}}{exp(I_0)+\sum_{r=1}^R\sum_{j=1}^Jy_j{_r}exp(\frac{x_j+x_r+b*log(P_j{_r})}{1-h})(\sum_{s=1}^Ry_j{_s}exp(\frac{x_j+x_r+b*log(P_j{_r})}{1-h}))^-{^h}} $$