We use the log law:

log an = n log a

So we can write the question as

y = ln x2 = 2 ln x

The derivative will be simply 2 times the derivative of ln x.

So the answer is:

`d/(dx)ln\ x^2=2 d/(dx)ln\ x=2/x`

We can see from the graph of y = ln x2 (curve in black, tangent in red) that the slope is twice the slope of y = ln x (curve in blue, tangent in pink).

graph ln x^2

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