Given a matrix $A$ and column vector $x$, what is the derivative of $Ax$ with respect to $x^T$ i.e. $\frac {d (Ax)} {d (x^T)}$, where $x^T$ is the transpose of $x$?

Be careful that directional derivative of a function is a scalar while gradient is a vector. The only difference between derivative and directional derivative is the definition of those terms.

I just learned a new trick when your independent variable is in more than two places within your formula: introduce a new (fake) parameter which will then disappear: $$\frac {\partial} {\partial x} y^TAx = \frac …

There is another way to solve the problem: Let $\mathbf {x}^ {n\times 1}= (x_1,\dots ,x_n)'$ be a vector, the derivative of $\mathbf y=f (\mathbf x)$ with respect to ...

From time to time, I come across with derivation operations which are executed with regard to a vector. For example, the least squares estimation method with more than one explanatory variables is

39 I have a doubt about the real meaning of the derivative of a vector field. This question seems silly at first but the doubt came when I was studying the definition of tangent space. If I understood well a …

The normal derivative is a directional derivative in a direction that is outwardly normal (perpendicular) to some curve, surface or hypersurface (that is assumed from context) at a specific point on the …

To calculate the derivative of the function $ g (x, y) = \|f (x, y)\|^2 $ with respect to $x$, you can use the chain rule and the derivative of the Euclidean norm $\|x\|$ as you mentioned.

7 I've already looked at Vector derivative w.r.t its transpose $\frac {d (Ax)} {d (x^T)}$, but I wasn't able to find the direct answer to my question in that question. What is the value of $$\frac {d} {dx} x^T\text { …

Feb 25, 2015 · Saying that, the tangent vector being the one which points the direction of movement of the radius vector of the curve at a particular point, when the magnitude is constant, the two vectors in …