Question

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

Answer 1

`d/dx((x-1)/(x+3)^2)=((x+3)^2-2(x-1)(x+3))/(x+3)^4`

Explanation:

The quotient rule states that `d/dx((f(x))/(g(x)))=(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2`

Applying this rule to the given quotient of 2 functions yields :

`d/dx((x-1)/(x+3)^2)=((x+3)^2*(1)-(x-1)*2(x+3))/(x+3)^4`