Can anyone please help me find the derivative of the ABC wrt B when:
A is say 3*3 matrix
B is 3*4 matrix
C is 4*4 matrix.
Let $\phi(B) = ABC$. $\phi$ is linear, so we have $\phi(B+\Delta) = \phi(B) + \phi(\Delta)$. It follows (Since $\phi(B+\Delta) - \phi(B) - \phi(\Delta) = 0$) that the derivative is $D\phi(B)(\Delta) = A \Delta C$.
This should be interpreted as the derivative of $\phi$ at the point $B$ in the direction $\Delta$ is $A \Delta C$.