## Derivative of real-valued function wrt. a vector

Hi

I need to find the derivative wrt. X of the following function:

$f(t,X) = e^{c(t)+d(t)^{\top} X + 0.5 X^{\top} \eta^{\top} Q \eta X}$

d(t) and X are (Nx1)-vectors, $\eta$ is (N1xN) and Q is (N1xN1).

To my knowledge the derivative become:

$f(t,X)_X = f(t,X) (d(t) + 0.5 ( \eta^{\top} Q \eta + \eta^{\top} Q^{\top} \eta)X)$

and if Q is symmetric it becomes:

$f(t,X)_X = f(t,X) (d(t) + \eta^{\top} Q \eta X)$

Is this correct?