Derivative with respect to vector

Let $x \in \mathbb{R}^{n}$ say a column vector. Let $f : \mathbb{R}^{n} \to \mathbb{R}$. The derivative of $f$ with respect to $x$ is the row vector given by $$ \begin{align*} \frac{\partial f}{\partial x} = \left( \frac{\partial f}{\partial x_{1}}, \cdots, \frac{\partial f}{\partial x_{n}} \right), \end{align*} $$

where $\frac{\partial f}{\partial x}$ is called the gradient of $f$.

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Published on May 7, 2021

Last revised on Apr 3, 2022