How do you find the first and second derivative of ln(x^3)?

1 Answer
Oct 19, 2016

d/dxln(x^3)=3/x

(d^2)/(dx^2)ln(x^3)=-3/x^2

Explanation:

Using the chain rule, the power rule, and the product rule, along with the derivative d/dx ln(x) = 1/x, we have

First Derivative:

d/dxln(x^3) = 1/x^3(d/dxx^3)

=1/x^3(3x^2)

=3/x

Second Derivative:

(d^2)/(dx^2)ln(x^3) = d/dx(d/dxln(x^3))

=d/dx(3/x)

=d/dx3x^(-1)

=3(-x^-2)

=-3/x^2