My text makes the statement:

"Note that expression (2) can be obtained formally by differentiating the integral in equation (1) with respect to z".

Equation (1) is:

$\displaystyle f(z) = \frac 1{2\pi i} \int _C \frac{f(s)ds}{s-z}$

Equation (2) is:

$\displaystyle f'(z) = \frac 1{2\pi i} \int _C \frac{f(s)ds}{(s-z)^2}$

the text then follows with a longer proof (in terms of limits etc) that the derivative of (1) exists and that it is (2).

My question is just what does "formally" mean in this context? Why can't I just differentiate (1) and say that (2) is proven?