Given the equation below, how should I treat the vector $a$?
$\frac{\partial}{\partial b} a \odot coth(Mb) $
$a\in R^n, b \in R^m $ and $M \in R^{n \times m}$
These are the chain rule steps I took:
$x = Mb$,
$x' = M$
$y = coth(x)$,
$y' = −csch^2(x)$
$z = a \odot y$,
$z' = a' \odot y + a \odot y'$ which is $a \odot cos(x)$
This doesn't feel right. What I am missing?
What should vector/matrix size should I expect to have in the end if n=2 and m=3?
Thanks a lot!