How do I find the derivative of #f(x)=ln(x^2)#?

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Answer 1 · 2018-03-02T02:37:53

Using Chain Rule, the answer is #2/x#

The Chain Rule is:

#(df)/(du) * (du)/(dx)#

where #f# is the general function

where #u# is the function within the function

Here, #f=ln(u)# and #u=x^2#

Now, we can substitute:

#d/(du)ln(u) * d/(dx)x^2#

Find the respective derivatives:

#=1/u * 2x#

Since #u=x^2#, we can substitute:

#1/x^2 * 2x#

#x# and #x# cancel out:

#1/x * 2#

#=2/x#