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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