Symbolic vector differentiation with Mathematica

[boeing_737]

Hi,

I am a new user of Mathematica (although I am reasonably familiar with MATLAB) and I am trying to differentiate a scalar wrt a vector Mathematica. ie, I want to check if
\begin{equation}
\phi = \textit{x}^{T} \textbf{A} \textit{y} \quad \mbox{where $\textit{x}$, $\textit{y}$ are vectors and $\textbf{A}$ is a symmetric matrix} \\
\frac{\partial{\phi}}{\partial{\textit{x}}} = \textbf{A} \textit{y}\\
\end{equation}

I am kind of lost and would appreciate some help on this.

Thanks
yogesh

 

[NateD]

In Mathematica, you can use the built-in function Derivative to differentiate a scalar with respect to a vector. You can define your function f[x_,y_,A_] as: f[x_,y_,A_] := x^T . A. yThen, you can calculate the partial derivative of f with respect to x with the following command:D[f[x,y,A],x]This should give you: Transpose[A].y