I know that the gradient of the least squares L2 norms is $\nabla\left \| Y-X\beta \right \|^2_2=2X^t(Y-X\beta)$
I have another similar function for which I calculated the gradient but I'm not sure if it is correct! $\nabla\left \| Y-X(e^\beta+1)\right \|^2_2=2X^t(Y-X(e^\beta+1))e^\beta$ Is the $e^\beta$ at the end correct?