Directional Derivative

Theorem

• Suppose that $f:{\mathbb{R}}^n\to \mathbb{R}$
• We can define a derivative $f$ at $x$ in direction $v$ to be:
• $Df(x)v=\frac{d}{dt}f(x+tv){|}_{t=0}={\lim }_{t\to 0}\frac{f(x+y)-f(x)}{t}$