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

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Answer 1 · 2016-10-19T00:57:21

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

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

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:

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

$=d/dx(3/x)$

$=d/dx3x^(-1)$

$=3(-x^-2)$

$=-3/x^2$

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