# Symbolic vector differentiation with Mathematica

• Mathematica
• boeing_737
In summary, to differentiate a scalar wrt a vector in Mathematica, you can use the Derivative function and define your function accordingly.
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

\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}\\

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

Thanks
yogesh

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

## 1. What is symbolic vector differentiation?

Symbolic vector differentiation is the process of finding the derivative of a vector-valued function with respect to one or more variables. It involves breaking down the vector function into its component functions and then taking the derivative of each component using the rules of differentiation.

## 2. How does Mathematica perform symbolic vector differentiation?

Mathematica uses the built-in function D to perform symbolic vector differentiation. This function takes in the vector function and the variables with respect to which the derivative is to be calculated, and returns the derivative as a vector function.

## 3. What are the advantages of using Mathematica for symbolic vector differentiation?

Mathematica has a powerful symbolic manipulation engine that allows it to handle complex vector functions and perform differentiation accurately and efficiently. It also offers a wide range of built-in functions and tools for analyzing and visualizing the results of differentiation.

## 4. Can Mathematica handle vector functions with multiple variables?

Yes, Mathematica can handle vector functions with multiple variables. It allows for differentiation with respect to one or more variables, and can also perform partial differentiation.

## 5. Are there any limitations to symbolic vector differentiation with Mathematica?

While Mathematica is a powerful tool for symbolic vector differentiation, it may not be able to handle extremely complex vector functions or functions with discontinuities. In these cases, it may be necessary to use numerical methods for differentiation instead.

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