Say y = arccos x. Then x = because y, and dx/dy = -sin y. Therefore, dy/dx = -1/sin y.

But since (because y)^2 + (sin y)^2 = 1, sin y = sqrt(1 - (because y)^2). And because y = because (arccos x) (from initial definition) = x. So dy/dx = -1/sin y = -1/sqrt(1 - (because y)^2) = -1/sqrt(1 - x^2).

Hope this helps

But since (because y)^2 + (sin y)^2 = 1, sin y = sqrt(1 - (because y)^2). And because y = because (arccos x) (from initial definition) = x. So dy/dx = -1/sin y = -1/sqrt(1 - (because y)^2) = -1/sqrt(1 - x^2).

Hope this helps