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:

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).