Differentiate sin-1x.
Differentiation.
Let y=sin-1x
∴siny=x
Differentiate the above equation with respect to x.
∴cosy·dydx=1⇒dydx=1cosy⇒dydx=11-sin2y∵sin2y+cos2y=1⇒dydx=11-x2∵siny=x
Hence, ddxsin-1x=11-x2,-1<x<1