Directional Derivative

Definition

The Directional Derivative at a point is the derivative along a specific direction $\mathbf{n}$. It can be calculated using the formula.

$$\boxed{{\nabla }_{\vec{n}}f=\vec{n}\cdot \nabla f}$$

Where, $||\vec{n}|{|}_2=1$

Limit definition

$$\frac{\partial f}{\partial \vec{n}}({\vec{x}}_o)=\underset{h\to 0}{\lim }\frac{f({\vec{x}}_o+h\cdot \vec{n})-f({\vec{x}}_o)}{h}$$