PX275 - A4a - directional derivatives

\vec{\nabla} ϕ = \frac{\partial ϕ}{\partial x} \hat{i} + \frac{\partial ϕ}{\partial y} \hat{j} + \frac{\partial ϕ}{\partial z} \hat{k}

$\vec{\nabla}$ gives the maximum vector gradient at any point
the derivative of a function, $ϕ$ , along any general direction, $\vec{u}$ is given by: $\vec{\nabla} ϕ \cdot \hat{u}$

\hat{u} = \frac{x \hat{i} + y \hat{j} + z \hat{k}}{\sqrt{x^{2} + y^{2} + z^{2}}}