Find the second derivative y = x^2lnx

First we use product rule

y=x^2lnx

dy/dx = x^2 d/dx (lnx) + lnx d/dx (x^2)

dy/dx = x^2 (1/x) + lnx (2x)

dy/dx = x + 2xlnx

now taking second derivative:

d2y/dx2 = 1 + 2[x (1/x) + lnx (1) ]

d2y/dx2 = 1 + 2[1+lnx]

1+2+2lnx

3+2lnx is the answer