What is the derivative of this function x+4/x-2??

Question

I have a Big test tomorrow and I would really appreciate if somebody could give me the answer because I already got it but I want to know if I'm right

 

MY ANSWER:  6/(x-2)^2

Answer 1

Let y = (x + 4) / (x - 2)

y'
= [(x - 2) d/dx (x + 4) - (x + 4) d/dx (x - 2)] / (x - 2)^2
= [(x - 2)(1) - (x + 4)(1)] / (x - 2)^2
= [(x - 2) - (x + 4)] / (x - 2)^2
= [x - 2 - x - 4] / (x - 2)^2
= -6 / (x - 2)^2

Hence, you were slightly wrong, though this could result in a huge marks loss.
Note that for any function of the form y = u / v, the derivative will be [v (du/dx) - u (dv/dx)] v^2