hmm
I was just looking at:
wolfram alpha for
d/dx \ f(x,y)^{g(x,y)} = f^{(1,0)}(x,y)g(x,y)f(x,y)^{g(x,y)-1} + g^{(1,0)}(x,y)f(x,y)^{g(x,y)}log(f(x,y) \\
d/dy \ f(x,y)^{g(x,y) } = f^{(0,1)}(x,y)g(x,y)f(x,y)^{g(x,y)-1} + g^{(0,1)}(x,y)f(x,y)^{g(x,y)}log(f(x,y) \\
d/dx \...