Find the derivative of the function. Simplify where possible G(x) = square(1-x^2) arccosx

G(x) = sqrt(1-x^2)*arccos(x)
G '(x) = sqrt(1-x^2)*(-1/sqrt(1-x^2)) + arccos(x)*((-x*(1-x^2))^(-1/2)
= [-x*arccos(x)]/(1-x^2)^(1/2)] - 1

There you are. When solving for the derivative of arc-trig functions, use your identities and implicit differentiation. That's how I got the derivative of arccos(x).

Hope that helps.