z'(x)=1/[1+(x^y)] * 1/2√(x^y) * yx^(y-1) =yx^(y-1) / {2√(x^y)[1+(x^y)] }
z'(y)=1/[1+(x^y)] * 1/2√(x^y) * lnx *x^y=(x^y) *lnx / {2√(x^y)[1+(x^y)] }