Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am reading through a book called "Matrix Differential Calculus" by Magnus and Neudecker. They go through taking the derivative of a vector in quadratic form that I need help with.

For [itex] \vec{x} [/itex] being a vector and A being a constant square matrix

[tex] \frac {d(\vec{x}^TA\vec{x})} {d\vec{x}} [/tex]

[tex]= \frac {d\vec{x}^T}{d\vec{x}}A\vec{x} + \vec{x}^TA\frac {d\vec{x}}{d\vec{x}} [/tex]

[tex]= (\frac {d\vec{x}^T}{d\vec{x}}A\vec{x})^T + \vec{x}^TA\frac {d\vec{x}}{d\vec{x}} {?}[/tex]

[tex]= \vec{x}^TA^T\frac {d\vec{x}}{d\vec{x}} + \vec{x}^TA\frac {d\vec{x}}{d\vec{x}} [/tex]

[tex]= \vec{x}^T(A+A^T)\frac {d\vec{x}}{d\vec{x}} [/tex]

[tex] \frac {d(\vec{x}^TA\vec{x})} {d\vec{x}}=\vec{x}^T(A+A^T) [/tex]

I don't understand how one can go from the second line to the third line

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Derivative of a vector function

**Physics Forums | Science Articles, Homework Help, Discussion**