The Chain Rule & Implicit Differentiation · Superchallenge problem

Let $F(t) = \displaystyle\int_0^{t}\ln(1 + ts)\,ds$ for $t > 0$. The variable $t$ enters both as the upper limit and inside the integrand. Treat $F(t) = G(t, t)$ with $G(u, v) = \displaystyle\int_0^{u}\ln(1 + vs)\,ds$ and use the chain rule to find $F'(1)$.