## Finding the score vector

Given that $y_1,...,y_n$ are independent with

$y_i\sim Bernoulli(\pi_i)$ and

$\pi_i=\Phi(\mathbf{x}_{(i)}^{\top}\beta)$ 1<i<n

$\Phi$ denotes the CDF of N(0,1), $\mathbf{x}_{(i)}$ is a known vector of explanatory variables for subject $i$, and $\beta_{(P+1)X1}$ is an unknown vector of parameters.

Then how do I derive the score vector. I have problem in finding the formula for taking the loglikelihood so as to attain the 1st derivative of ${l}(\pi|Y)$. Is there a formula for a $\Phi(.)$ as above to begin with?