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

By fundamental theorem of calculus we have $$\frac{d}{dx}\int_a^xf(t) dt=f(x)$$ and by chain rule we will get $$F'(x)=\frac{1}{\ln x^3}\cdot(3x^2)=\frac{3x^2}{3\ln x}=\frac{x^2}{\ln x}$$
