The derivative of arcsin x is 1/√1-x². This can be written as d/dx(arcsin x) = 1/√1-x² or d/dx(sin-1x) = 1/√1-x². To derive the derivative of arcsin, assume that y = arcsin x, then sin y = x. Differentiating both sides with respect to y, then cos y = dx/dy. Taking reciprocals, dy/dx = 1/(cos y) = 1/√1 - sin²y = 1/√1-x².