Why the quotient rule subtracts

(uv) = vu -uv v2 (v 0) y= uv u=yv u =y v+yv. Rearranging and replacing y gives the rule; the subtraction accounts for the denominator changing. Method Keep numerator and denominator roles fixed; form denominator times numerator derivative minus numerator times denominator derivative; divide by the squared denominator; preserve original exclusions. Example y= x+1x-1, y = (x-1)-(x+1)(x-1)2=- 2(x-1)2, x 1 Exam check Reversing the numerator subtraction reverses the answer’s sign. Cancelling a factor does not restore an excluded input.