Find the differential of y=arcsinx

To differentiate we must use implicit differentiation. So: siny=x .Differentiating both sides we get (dy/dx)cosy=1, so (dy/dx)=1/cosy . Using the common identity (sin²(y)+cos²(y)=1) we can rewrite the denominator so we have: (dy/dx)=1/((1-sin²y)^(1/2)) we can then substitute sin y with the identity we have in the first line of working: (dy/dx)=1/(1-x²)^(1/2)