Hi, "turbozz."

I am puzzled.

If y = sin(x), and P is the inverse of this function, then P = x = arcsin(y).

And the range changes: instead of being stated in terms of x, it is stated in terms of y: [1, -1].

By definition, the derivative of the arcsin function is:

Why is the derivativenotthis standard definition?

Are you looking for a derivative at one particular point?