y′ =[(arcsinx)′arccosx-arcsinx(arccosx)′]/(arccosx)^2 ={[1/√(1-x^2)]arccosx+[1/√(1-x^2)]arcsinx}/(arccosx)^2 =[1/√(1-x^2)](arccosx+arcsinx)/(arccosx)^2 =2π/[(arccosx)^2·√(1-x^2)]