I am trying to define the gradient of $x^Ty$ with respect of $x$ where both $x, y$ are column vectors $\in \mathbb{R}^m$.
$\frac{\partial x^Ty}{\partial x} = [\frac{\partial x^Ty}{\partial x_1} , \frac{\partial x^Ty}{\partial x_2} , ... , \frac{\partial x^Ty}{\partial x_m}] = [y_1, y_2, ..., y_m] = y^T$
or is it
= $[\frac{\partial x^Ty}{\partial x_1} , \frac{\partial x^Ty}{\partial x_2} , ... , \frac{\partial x^Ty}{\partial x_m}]^T = [y_1, y_2, ..., y_m]^T = y$
I am quite confused since I haven't been exposed to multivariate calculus before.