# Derivative of a function

• Oct 17th 2011, 01:06 PM
regdude
Derivative of a function
Hi!
Usually in class there are examples when you are able to find these derivatives by derivativating both sides and at the end you can simply cross out some parts and get y' simply by dividing.
In this example I can't figure out what to do next:
ImageShack&#174; - Online Photo and Video Hosting
I don't ask to do all the work, leave some for me too :)
This is as far as I got, maybe I made a mistake so now can't see anything to divide.
Any ideas?

[EDIT]
Found one mistake, but doesn't change much, not (x+y)^2 but (x-y)^2
• Oct 17th 2011, 01:20 PM
Plato
Re: Derivative of a function
Quote:

Originally Posted by regdude
ImageShack&#174; - Online Photo and Video Hosting
I don't ask to do all the work, leave some for me too :)
This is as far as I got, maybe I made a mistake so now can't see anything to divide.

I would rewrite it as:
$\displaystyle \left( {x^2 + \frac{{2y}}{{x^2 + y^2 }} + \frac{2}{{1 + (x + y)^2 }}} \right)y' = \frac{2}{{1 + (x + y)^2 }} - \frac{{2x}}{{x^2 + y^2 }} - 2xy$

Solve for $\displaystyle y'$.
• Oct 17th 2011, 01:25 PM
regdude
Re: Derivative of a function
Aww... I forgot that you can write (a+b)/c = a/c + b/c
Thanks!