Differentiate Inverse Sine

This tutorial explain how to differentiate inverse sine, this applies when using radians.

begin with

y = sin^-1 x
bring sin^-1 across to become sin
sin y = x
differentiate
cos y dy/dx = 1
note that the derivative of sint wrtt is cos t as explained in an earlier tutorial and by the chain rule when we differentiated sin y it became cosy time dy/dx as we are differnetiatiny a y and the derivative of y is dy/dx

then make dy/dx the subject

dy/dx = 1/cosy

We know the identity
sin²t + cos²t = 1
so we can wrtie
cos t =√(1 - sin²t)

we can now put this into the expression for dy/dx to get
dy/dx = 1/√(1 - sin²y)
but we know from the second line that sin y = x so

dy/dx = 1/√(1 - x²)