I dont understand why when the derivative of arcsine is taken it is

http://www.math.brown.edu/UTRA/trigderivs/image017.gif. Can someone help me understand please!

Thank you!

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- Jan 27th 2009, 08:43 AMgabet16941derivative of arcsine
I dont understand why when the derivative of arcsine is taken it is

http://www.math.brown.edu/UTRA/trigderivs/image017.gif. Can someone help me understand please!

Thank you! - Jan 27th 2009, 09:30 AMChris L T521
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? - Jan 27th 2009, 09:37 AMgabet16941
Yes thank you very much!