I dont understand why when the derivative of arcsine is taken it is
. Can someone help me understand please!
Thank you!
Note that is differentiable on the interval and is differentiable on the interval
Let .
Now, implicitly differentiating both sides, we have
We can divide through by because on the interval . Also on the interval . Now, we can use the identity to find :
Thus, we see that
Since we let , it now implies that
Does this make sense?