How do you find the first and second derivative of ln(x3)?

1 Answer
Oct 19, 2016

ddxln(x3)=3x

d2dx2ln(x3)=3x2

Explanation:

Using the chain rule, the power rule, and the product rule, along with the derivative ddxln(x)=1x, we have

First Derivative:

ddxln(x3)=1x3(ddxx3)

=1x3(3x2)

=3x

Second Derivative:

d2dx2ln(x3)=ddx(ddxln(x3))

=ddx(3x)

=ddx3x1

=3(x2)

=3x2