Answer:
d^2y/dx^2 = 5x + 6x lnx
Step-by-step explanation:
f(x) = y = 2 + x^3 lnx
Differentiating a constant (2) = 0
Differentiating x^3 lnx = x^3(1/x) + lnx(3x^2) = x^2 + 3x^2 lnx
dy/dx = 0 + x^2 + 3x^2 lnx = x^2 + 3x^2 lnx
Differentiating x^2 = 2x
Differentiating 3x^2 lnx = 3x^2(1/x) + lnx(6x) = 3x + 6x lnx
d^2y/dx^2 = 2x + 3x + 6x lnx = 5x + 6x lnx
