$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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Let $A\subseteq\mathbb{R}^n$ be open, $f:A\to\mathbb{R}^m$, and $\vec{u}$ a unit vector. The directional derivative of $f$ in the direction $\vec{y}$, denoted $D_{\vec{u}}$, is defined as $$\begin{align*} D_{\vec{h}}(\vec{a})=\lim_{h\to\0}\frac{f(\vec{a}+h\vec{u})-f(\vec{a})}{|h|} \end{align*}$$

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Let $A\subseteq\mathbb{R}^n$ be open, $f:A\to\mathbb{R}^m$, and $\vec{u}$ a unit vector. The directional derivative of $f$ in the direction $\vec{y}$, denoted $D_{\vec{u}}$, is defined as $$\begin{align*} D_{\vec{h}}(\vec{a})=\lim_{h\to\0}\frac{f(\vec{a}+h\vec{u})-f(\vec{a})}{|h|} \end{align*}$$

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definition
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definition
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hypothesis
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Let $A\subseteq\mathbb{R}^n$ be open, $f:A\to\mathbb{R}^m$, and $\vec{u}$ a unit vector. The directional derivative of $f$ in the direction $\vec{y}$, denoted $D_{\vec{u}}$, is defined as $$\begin{align*} D_{\vec{h}}(\vec{a})=\lim_{h\to\0}\frac{f(\vec{a}+h\vec{u})-f(\vec{a})}{|h|} \end{align*}$$

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Let $A\subseteq\mathbb{R}^n$ be open, $f:A\to\mathbb{R}^m$, and $\vec{u}$ a unit vector. The directional derivative of $f$ in the direction $\vec{y}$, denoted $D_{\vec{u}}$, is defined as $$\begin{align*} D_{\vec{h}}(\vec{a})=\lim_{h\to\0}\frac{f(\vec{a}+h\vec{u})-f(\vec{a})}{|h|} \end{align*}$$

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