yup i got ur mistake in the 1 st principal u have used , u have taken h= -m , ok m tends to 0 . but u forgot that the limit is always applicable with the quantity h always +ve !!!! m is definitely -ve
so d/dx of f(x) = f(x) - f(x-h) /h and not that u have written ! when u express it like this the minus minus will cancel and give the same result !!!