$\displaystyle f(x,t)=\int_{0}^{t}\frac{1}{1-s}dx$

s is a dummy for t

x is a function of t

how can I find the partial derivatives? I think $\displaystyle f_{x}(x,t)=\frac{1}{1-t}$ - is this right?

But I have no idea how to find $\displaystyle f_{t}(x,t)$

Thanks for any help