How do you calculate the derivative of cos inverse x?

When differentiating cos inverse x, the typical method is to make y equal to cos inverse x.By taking cos of both sides: x = cosy.You can then differentiate with respect to y, obtaining that: (dx/dy) = - sinyUsing our knowledge of derivatives, we now know that: (dy/dx) = -1/(siny)From x = cosy, x^2 = (cosy)^2                  = 1 - (siny)^2          (siny)^2 = 1 - x^2            siny = (1-x^2)^(1/2)Combining this with the equation stating (dy/dx), we get:     (dy/dx) = (-1)/((1-x^2)^(1/2))Since y is equal to the cos inverse function, this is now equal to the derivative of cos inverse x.