derivative of rotation matrix w.r.t euler angles (Z-Y-X)

Question

I have the states:

$X = \begin{bmatrix} \alpha_{1} & \beta_{1} & \gamma_{1} & \alpha_{2} & \beta_{2} & \gamma_{2}\end{bmatrix}^{\mathsf{T}}$

and suppose I have the relation using ZYX Euler angles:

$h(X) = Rot(\alpha_{2}, \beta_{2}, \gamma_{2})Rot(\alpha_{1}, \beta_{1}, \gamma_{1})^{\mathsf{T}}$

Now, how do I get the jacobian $\nabla h$?