Answer
$$\frac{3}{{{x^4}}}$$
Work Step by Step
$$\eqalign{
& \frac{d}{{dx}}\int_2^{{x^3}} {\frac{{dp}}{{{p^2}}}} \cr
& {\text{using The Fundamental Theorem }}\left( {{\text{part 1}}} \right) \cr
& A\left( x \right) = \int_a^x {f\left( t \right)dt{\text{ }} \to {\text{ }}} A'\left( x \right) = \frac{d}{{dx}}\int_a^x {f\left( t \right)dt} = f\left( x \right) \cr
& {\text{the upper limit is }}{x^3},{\text{ so is needed to apply the chain rule}} \cr
& \frac{d}{{dx}}\int_2^{{x^3}} {\frac{{dp}}{{{p^2}}}} = \frac{{dy}}{{dx}} = \frac{{dy}}{{du}}\frac{{du}}{{dx}} \cr
& {\text{with }}u = {x^3} \cr
& = \left( {\frac{d}{{du}}\int_0^u {\frac{{dp}}{{{p^2}}}} } \right)\frac{d}{{dx}}\left( {{x^3}} \right) \cr
& = \left( {\frac{d}{{du}}\int_0^u {\frac{{dp}}{{{p^2}}}} } \right)\left( {3{x^2}} \right) \cr
& {\text{by the fundamental theorem }}\left( {{\text{part 1}}} \right) \cr
& = \left( {\frac{1}{{{u^2}}}} \right)\left( {3{x^2}} \right) \cr
& = \left( {\frac{1}{{{{\left( {{x^3}} \right)}^2}}}} \right)\left( {3{x^2}} \right) \cr
& = \frac{3}{{{x^4}}} \cr} $$
