What is the derivative of arcsin x

Proof for the derivative of asin (x)

We prove the derivative of the arcsine, with complete derivation and explanation.

Proof and explanation

It should be proven that for a real number x, for which we have -1

The statement implies that if we apply the sine function to both sides of the equation, we get the following equation: .

The derivative of x is therefore

The reciprocal of this is

From the trigonometric identity of the mutual representation, we know that

If we don't solve this identity cos (y) and take the roots on both sides, we get:

Since cos (y) ≥ 0 on the interval we need to take the positive square root. So we have:

It follows:

After we resubstitute sin (y) by x, our end result is: