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#