I am sorry Tonio,
That was a typo, Its suppose to be the upper case Z. But I was wondering, it I could use such chain rule and get the dh/dt and dz/dt out of the integral like that.
Then I have a predefined function of which is x = (1+(ba)^n)^-(1+1/n). So. Now I can differentiate this function w.r.t. a, and then integrate within the limit of (0 to Z).
Is this mathematically legitimate?. I would be grateful If I could get some help in solving this.