Deriving Simple Tax Multiplier with Calculus (Macro Ugrad) It looks like I am making a calculus mistake here, and I am really banging my head against the wall.

Here is my work:

[img]http://i.imgur.com/e19Fmrx.jpg[/img]

I know I should be getting $dY/dT=-(MPC)/(1-MPC)$, where $MPC=dC/dY$
If this is at all helpful here is a picture of page 295 in 7th edition of Macroeconomics By Mankiw that briefly describes the process. 

[img]http://i.imgur.com/VKPbZbz.jpg[/img]

It is confusing to me that he uses $C'$ for both terms on right-hand side when $C$ is composed of two arguments, so I decided to use Leibniz notation to see what is going on.

Thanks for help! 
Chris
So here $C$ is a function with the argument $Y-T$, like $C=f(Y-T)$

So differentiate the equation: $dY=C' * (dY-dT)$

The result immediately follows like in the book. 

The reason you don't do the partial derivative is that C has only one argument - while Y and T are in there, it only takes in 1 input.