So basically the function is: f(x) = x
^{2} (x
^{2} + 1)
^{-3}.
I have to use the quotient rule to differentiate it. I just started derivatives, so I don't quite understand it. I've had like 5 different tutors or people explain this specific problem, but I still don't understand it and they all got frustrated with me when I didn't understand.
I understand d/dx (u/v) = (v (du/dx) - u (dv/dx)) / (v2) is the quotient rule. I understand this no problem.
u = x
^{2} v = (x
^{2} + 1)
^{3}
f(x) = (x
^{2})/(x
^{2}+1)
^{3}
= ((x
^{2} + 1)
^{3} (2x) - (x
^{2}) 3(x
^{2} + 1)
^{2} (2x))/(x
^{2} + 1)
^{6} I understand this because it's just using the quotient rule and deriving what you can in there.
= ((x
^{2} + 1)
^{3} (2x) -6x
^{3} (x
^{2} + 1)
^{2}) / (x
^{2} + 1)
^{6} This is just simplifying, so I understand this....
Then after there is where the tutors lose me, I've had the tutors come to different answers too, so I have no idea, super frustrated.