Originally Posted by

**lampak** I don't know what I'm doing wrong (but I know I'm doing something) but I keep getting these two derivatives the same:

$\displaystyle

(\tfrac{1}{1-x})'=\tfrac{-1}{(1-x)^2}(-1)=\tfrac{1}{(1-x)^2}

$

$\displaystyle

(\tfrac{x}{1-x})'=\tfrac{x'(1-x)-x(1-x)'}{(1-x)^2}=\tfrac{1-x+x}{(1-x)^2}=\tfrac{1}{(1-x)^2}

$

But two derivatives can be the same only if the functions differ only with a constant!

I know, I must be making some terribly stupid mistake somewhere. But I can't find it.