How to differentiate y=arcsinx (Implicit Differentiation)

How to differentiate y=arcsinx (Implicit Differentiation)

y=arcsinx

siny=x

cosy * dy/dx = 1

dy/dx = 1/cosy

But...

(siny)^2+(cosy)^2=1

(cosy)^2=1-(siny)^2

(cosy)^2=1-x^2

cosy=√(1-x^2)

Therefore:

dy/dx = 1/(√(1-x^2))

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