Question

How do you use the quotient rule to differentiate `y=(x+3)^2/(x-1)`?

Answer 1

`f= (x+3)^2, g=x-1->f'=2(x+3)*1=2x+6,g'=1 ->y'=((gf'-fg')/g^2) =( (x-1)(2x+6)-(x+3)^2)/(x-1)^2 =(2x^2+4x-6-x^2-6x-9)/(x-1)^2 = (x^2-2x-15)/(x-1)^2`

Explanation:

Separate f and g and find their derivatives then plug it in to the quotient rule as shown above