Finding Higher-Order Derivatives In Exercise, find the second derivative of the function.

f (x) = 2 + x3 ln x

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