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# differentiate y = sin^(-1)x

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1. i tried using chain rule, with u = sin x

I get -cosx/sin x

1/(1-x²)^1/2
2. You must not confuse as . The first means the inverse sin function not the recipricol.

To differentiate the inverse sin function you do the following:

little hint:
Spoiler:
Show

and use implicit differentiation

full working:
Spoiler:
Show

But you know that
therefore
and you also know that
therefore
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\frac{dy}{dx}=\frac{1}{\sqrt{1-x^2}

3. y=sin-1x

sin y = x
cos y = dx/dy
dy/dx=1/cos y

and....

sin y=x
sin^2y=x^2
1-cos^2y=x^2
(1-x^2)^1/2= cos y sub that into 1/cos y

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