On Wikipedia, the following formula is given:
$$\frac {F^\prime(s)}{F(s)} = - \sum_{n=1}^\infty \frac{f(n)\Lambda(n)}{n^s}$$
I understand the proof for the zeta-function, but not for the Dirichlet Series of a multiplicative function. I have to proof this formula especially for the $L$-function of modular forms and tried to do so with the Euler product but have not managed it yet.