# Directional Derivative – Calculating Derivative in the direction of a normal to a surface – Exercise 4307

Exercise

Find a level surface of the scalar field

$$u=3x^2+5y^2+z^2$$

At the point (1,-1, 2) and calculate the directional derivative of u at point and in the normal direction to the surface.

$$3x^2+5y^2+z^2=12$$
$$D_{\vec{a}}u(1,-1,2)=\sqrt{152}$$