Derivative of integral in interval Let $$F(x)=\int_{2}^{x^3}\frac{dt}{\ln t}$$ and $x$ is in $(2,3)$. Find $F'(x)$. Can somebody give me idea how to do this?
Thank you

if $F(x)=\int_{a}^{x}h(t)dt$ then $F'(x)=h(x)$ from fundamental theorem.
Now $\int_{a}^{g(x)}h(t)dt=F(g(x))$
so, $\frac{d(F(g(x)))}{dx}=F'(g(x))g'(x)$ by chain rule. 
