Answer:
d^2y/dx^2 = 2/x^2
Step-by-step explanation:
f(x) = y = In x/x^3 + x
Differentiating x/x^3 = [x^3(1) - x(3x^2)]/(x^3)^2 = (x^3 - 3x^3)/x^6 = -2x^3/x^6 = -2/x^3
Assuming u = x/x^3
In x/x^3 = In u
Differentiating In u = 1/u = x^3/x = x^2
Differentiating x = 1
dy/dx = x^2(-2/x^3) + 1 = -2/x +1
Differentiating -2/x = 2/x^2
Differentiating a constant (1) = 0
d^2y/dx^2 = 2/x^2 + 0 = 2/x^2
