Proof Of The Derivative Of Arccos(x)

First lets start with a right-angled triangle where one of the angles is y. Lets say the adjacent side is of length x and that the hypotenuse is of length 1:

Using the triangle above, we can say:

We already know that the derivative of x with respect to x is 1:

Since x = cos(y):

Using the chain rule:

And we already know what sin(y) is equal to (look above):

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