Calculating dy/dx for Inverse Sine Functions

[Prasad Nemade]

Y= sin^(-1)⁡〖x+ sin^(-1)⁡√((1-x^2 ) 〗
Please show steps for it...

 

[superg33k]

I think this'll about do it:

http://www.wolframalpha.com/input/?...)^(-1)&f3=x&f=Derivative.derivativevariable_x

 

[HallsofIvy]

Since this problem has nothing to do with "differential equations", I am moving it.

 

[HallsofIvy]

Y= sin^(-1)⁡〖x+ sin^(-1)⁡√((1-x^2 ) 〗
Please show steps for it...

There are some funny looking symbols in there. I will assume that the function is
$$y= sin^{-1}(x+ sin^{-1}(\sqrt{1- x^2}))$$

Let $u(x)= 1- x^2$, $v(u)= \sqrt{u}= u^{1/2}$, and $w(v)= sin^{-1}(v)$. Then use the chain rule.

 

[Redbelly98]

Moderator's note:

This looks like homework, or at the very least a textbook-style problem. Even if it's for independent study and not assigned coursework, this thread should in the Homework & Coursework Questions forums.

I am moving it to the Calculus & Beyond homework forum. Please note that the usual rules for homework help are in effect.

EDIT: in case it isn't clear -- we should let the OP reply with an attempt at solving this before offering further help.