2.3.25 Gradient and directional derivative

Problem: For given scalar fields \( u, v \) find: a) the derivative of \( u \) in the direction of \( \vec{e} \) at point \( M \), b) the angle between gradients \( u \) and \( v \) at points \( N \) and \( M \), where \[ \begin{array}{l} v=6 \sqrt{6} x^{3}-6 \sqrt{6} y^{3}+2 z^{3}, \quad u=\frac{x z^{2}}{y} \\ M(1 ; 1 ; \sqrt{6}), \quad N\left(\frac{1}{\sqrt{6}} ; \frac{1}{\sqrt{6}} ; 1\right), \quad \vec{e}=(2 ; 3 ; 4) . \end{array} \]