Sorry, you're not making a lot of sense, so far.
You define "Y". Is that the same as the subsequently defined "y" in dy/dx?
You then have Cos(arcsinx0) in the numerator. What is that? Is the zero (0) extraneous? Did you mean cos(arcsin(x)) EVALUATED at x = 0 after finding the derivative?
Let's just try a wild guess:
cos(arcsin(x))
This needs a few things:
-- A Right Triangle,
-- Some Basic Trig Functions, and
-- The Pythagorean theorem
Draw a Right Triangle.
Label one of the Acute Angles, A
arcsin(x) gives an angle, the angle A, such that sin(A) = x.
Label two sides of your triangle so that sin(A) = x. That is, label the opposite leg, 'x', and label the hypotenuse '1'.
Calculate the adjacent leg, sqrt(1 - x^2)
Write an expression for cos(A). You should get sqrt(1-x^1)/1 or just sqrt(1-x^1).
Now, IF your original expression was supposed to be:
cos(arcsin(x))/sqrt(1-x^2)
That is pretty unfortunate, since that expression is equal to one (1), by the previous demonstration.
OK, another guess. The question is simply to find:
(d/dx)sin(arcsin(x)).
Using the chain rule, one gets, cos(arcsin(x))*(1/sqrt(1-x^2)), and we are left with proving this equal to unity. Hey, we did that already (See Above).
