How do I take the partial derivative of bivariate normal cdf and bivariate normal pdf with its arguments (i.e. $x\_{1}$ ,$x\_{2}$ , and $\rho$ in the following equations)?

\begin{equation}
y=\Phi(x\_{1},x\_{2},\rho)
\end{equation}

\begin{equation}
z=\phi(x\_{1},x\_{2},\rho)
\end{equation}

where $x\_{1}$ is normally distributed with mean 0 and variance 1 and $x\_{2}$ is normally distributed with mean 0 and variance 1. $\rho$ is the correlation between $x\_{1}$ and $x\_{2}$.