How Do You Differentiate an Equation Involving Arcsin?

[mlowery]

I need to differentiate D (the first equation). In this equation, there is an arcsin. I am not sure what to do about this. Well . . . just have a look:
http://www.mlowery.0nyx.com/differentiate.jpg"
If the browser says access denied, copy and paste the URL into a new browser window and it will work.
I do not know whether or not I used the chain rule correctly and I have never differentiated arcsin before.
Yes, this is part of my homework. But it is a small part of a larger project. I know exactly what I have to do to complete the project. I have just spent 3 hours attempting to differentiate this. Please do not assume I am simply trying to get a free answer.

 

[TD]

It looks good, perhaps you could simplify it a bit but your derivative seems correct

 

[mlowery]

Thanks. It took me a while to simplify, but here is is:
http://www.mlowery.0nyx.com/differentiate.jpg"

Once again, if access is denied, copy and paste the URL into a new browser.

 

[mlowery]

Thanks. It took me a while to simplify, but here is is:
http://www.mlowery.0nyx.com/differentiate.jpg"

Once again, if access is denied, copy and paste the URL into a new browser.

 

[Focus]

I can't see the image, it appears to be empty but...

$$y=arcsin(x)$$
$$x=sin y$$
$$\frac{dx}{dy}=cos y$$
$$\frac{dy}{dx}=\frac{1}{ cos y}$$
$$\frac{dy}{dx}=\frac {1}{\sqrt{1-sin^2 y}}$$
$$\frac{dy}{dx}= \frac {1}{\sqrt{1-x^2}}$$