If arcsin ln ,x y= then dydx =

The question seems to be asking for the derivative of a function, specifically the derivative of y with respect to x (dy/dx) where y = arcsin(ln(x)).

Here are the steps to find the derivative:

1. Identify the outer function and the inner function. In this case, the outer function is arcsin(u) and the inner function is ln(x).

2. Apply the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, times the derivative of the inner function.

3. The derivative of arcsin(u) with respect to u is 1/√(1 - u²). So, the derivative of arcsin(ln(x)) with respect to ln(x) is 1/√(1 - ln²(x)).

4. The derivative of ln(x) with respect to x is 1/x.

5. Multiply the results from steps 3 and 4 to get the derivative of the original function with respect to x.

So, dy/dx = (1/√(1 - ln²(x))) * (1/x).