Help with the quotient rule of derivatives, involving negative exponents.

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.

http://img253.imageshack.us/img253/8128/mathup.png

Re: Help with the quotient rule of derivatives, involving negative exponents.

Quote:

Originally Posted by

**bnosam** 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.

http://img253.imageshack.us/img253/8128/mathup.png

What you have is correct. If you want, you can take out a common factor of $\displaystyle \displaystyle \begin{align*} (x^2 + 1)^2 \end{align*}$ and cancel it, and then simplify whatever is left...

Re: Help with the quotient rule of derivatives, involving negative exponents.

Quote:

Originally Posted by

**Prove It** What you have is correct. If you want, you can take out a common factor of $\displaystyle \displaystyle \begin{align*} (x^2 + 1)^2 \end{align*}$ and cancel it, and then simplify whatever is left...

Yeah, I was over thinking it...silly silly silly. Thanks, though!