Create Symbolic Matrix from Symbolic Vector

I have a 4x4 homogeneous transformation matrix h which is a function of theta and phi, two angles. For some vector v_a, let's say, I want to find the change in a vector v_b given the velocities of v_a. Thus, I can take the transform h and multiply it times v_a which gives three equations relating the position of vector v_a to v_b via a transform. If I differentiate each of these equations with respect to time, my goal is derive a matrix such that the column vector of [x_a_dot; y_a_dot; z_a_dot; theta_dot; phi_dot] multiplied by this matrix gives the velocities of v_b in the form [x_b; y_b; x_b]. Note that the column vector above I wish to express as arbitrary functions of time. I have already done these calculations by hand though I wish to use MATLAB to double check my work. Is this possible with the symbolic math toolbox? The matrix for h is below and z0 is considered a constant. Thank you in advance!

 h = [ cos(phi(t))*cos(theta(t)), cos(theta(t))*sin(phi(t)), -sin(theta(t)),        z0*sin(theta(t))]
[              -sin(phi(t)),               cos(phi(t)),              0,                       0]
[ cos(phi(t))*sin(theta(t)), sin(phi(t))*sin(theta(t)),  cos(theta(t)), -z0*(cos(theta(t)) - 1)]
[                         0,                         0,              0,                       1]