Differentiating the expressions using leibniz rule

Question

Problem: ≤ ≥ ƒ ∫

1. Verify that the solution of u'' = ƒ(x),u(0) = 0, u(1) = 0 is given by

      u(x) = ∫¹₀ k(x,y)ƒ(y)dy

                         {y(x-1) 0≤yWhere k(x,y) =                           
                         {x(y-1) 0≤y

Use Liebniz rule to differentiate the expression u(x) = ∫¹₀ y(x-1)ƒ(y)dy+∫¹_x x(y-1)(y)dy twice with resect to x.