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).
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