leibniz rule

[gais]

If ∫(u to v) e^(-t^2) dt = x
and
u^v = y

Find
(∂u/∂x) at y constant, (∂u/∂y) at x constant
and (∂y/∂x) at u constant
at u= 2, v=0.

How to do this problem? pls explain in detail

I think its leibniz rule. but dont understand how to solve this problem.....

Thank you..