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

Recall that:
$$F(u) = \int_a^u f(t)\ dt\implies \frac{d}{du}F(u) = f(u)$$
We are now interested in
$$\frac{d}{dx}F(u(x)) = \frac{d}{dx}\int_a^{u(x)}f(t)\ dt = \left(\frac{d}{du}F(u(x))\right)\frac{du}{dx} = f(u)\frac{du}{dx} = \dots$$
