Using the product rule for the second order derivative:
d^2/dx^2 (x^3logx) = (d^2/dx^2 x^3)logx +2 (d/dx x^3)(d/dx logx) + x^3(d^2/dx^2 logx)d2dx2(x3logx)=(d2dx2x3)logx+2(ddxx3)(ddxlogx)+x3(d2dx2logx)
d^2/dx^2 (x^3logx) = 6xlogx +2 xx 3x^2 xx 1/x + x^3(-1/x^2)d2dx2(x3logx)=6xlogx+2×3x2×1x+x3(−1x2)
d^2/dx^2 (x^3logx) = 6xlogx +6x -xd2dx2(x3logx)=6xlogx+6x−x
d^2/dx^2 (x^3logx) = 6xlogx + 5xd2dx2(x3logx)=6xlogx+5x
d^2/dx^2 (x^3logx) = x(6logx + 5)d2dx2(x3logx)=x(6logx+5)