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

• Sep 4th 2012, 06:46 PM
bnosam
Help with the quotient rule of derivatives, involving negative exponents.
So basically the function is: f(x) = x2 (x2 + 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 = x2 v = (x2 + 1)3

f(x) = (x2)/(x2+1)3

= ((x2 + 1)3 (2x) - (x2) 3(x2 + 1)2 (2x))/(x2 + 1)6 I understand this because it's just using the quotient rule and deriving what you can in there.

= ((x2 + 1)3 (2x) -6x3 (x2 + 1)2) / (x2 + 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
• Sep 4th 2012, 06:59 PM
Prove It
Re: Help with the quotient rule of derivatives, involving negative exponents.
Quote:

Originally Posted by bnosam
So basically the function is: f(x) = x2 (x2 + 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 = x2 v = (x2 + 1)3

f(x) = (x2)/(x2+1)3

= ((x2 + 1)3 (2x) - (x2) 3(x2 + 1)2 (2x))/(x2 + 1)6 I understand this because it's just using the quotient rule and deriving what you can in there.

= ((x2 + 1)3 (2x) -6x3 (x2 + 1)2) / (x2 + 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 \begin{align*} (x^2 + 1)^2 \end{align*} and cancel it, and then simplify whatever is left...
• Sep 4th 2012, 07:27 PM
bnosam
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 \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!