Deriving the Wheatstone Bridge Equation with Respect to R3 - Math Nerd Help

[mhrobson]

I need to derive the following equation with respect to R₃. This is the equation for a Wheatstone bridge. Unfortunately I am not very good at derivations. Here is the equation:
V_O=((R₃/(R₂+R₃))-(R₄/(R₁+R₄)))V_S

I came up with the following answer but was told that it is wrong:
dV_O/dR₃ = ((1/(R₂+R₃))-(R₃/(R₂+R₃)²)V_S

If you want to be a real sport, set R₁=R₃ and derive the same expression.

 

[g_edgar]

Suppose y=((x/(12+x))-(4/(12+4)))\cdot 6, can you do dy/dx now?