Identity for Matrix*Vector differentiation w.r.t a vector

[MattF1]

I have

J - matrix
x and y - vector

d [ J(x) y(x)] / dx

I can multiply the matrix and vector together and then differentiate but I think for my application it would be better to find an identity like

{d [ J(x) y(x)] / dx } = J(x) d y(x) / dx + d J (x) / dx y(x)

I am not sure if this identity is right though?

Any help appreciated

 

[Orodruin]

Yes, you can use the product rule just as you did.