Finding Symbolic Matrix Derivative

I have the following Matrix and I wish to find its derivative,

A =

Please note that ϕ and θ in this matrix are functions of time t.

I have the following MATLAB code,

syms phi theta t real
A = [1 , 0 , -sin(theta) ;...
    0 , cos(phi) , cos(theta) * sin(phi) ;...
    0 , -sin(phi) , cos(phi) * cos(theta)];
Adot = diff(A); % this isn't giving the result I expect

So I tried,

 syms phi theta t real
A = [1 , 0 , -sin(theta) ;...
    0 , cos(phi) , cos(theta) * sin(phi) ;...
    0 , -sin(phi) , cos(phi) * cos(theta)];
phi(t) = phi;
theta(t) = theta;
Adot = diff(A , t); % this also isn't working

The result I want is,

Please help me to get this result.

Answer 1

[Paul]

Declare theta and phi as functions, and then substitute after differentiating A

syms phi(t) theta(t) phi_dot(t) theta_dot(t)
A=[1 0 -sin(theta);0 cos(phi) cos(theta)*sin(phi);0 -sin(phi) cos(phi)*cos(theta)]

A(t) = 

subs(diff(A,t),diff([phi(t) theta(t)]),[phi_dot(t) theta_dot(t)])

ans(t) = 

Note that this result is not the same as the expected result in the question, which appears to have some terms that are incorrect.