# Directional Derivative – Calculating Derivative oriented by angles – Exercise 4299

Exercise

Calculate the directional derivative of the function

$$u=xyz$$

At point (1,1,1) and in the vector direction

$$\vec{a}=(\cos\alpha,\cos\beta,\cos\gamma)$$

What is the size of the gradient of the function at this point?

$$D_{\vec{a}} u(1,1,1)=\cos\alpha+\cos\beta+\cos\gamma$$
$$|\nabla u(1,1,1)|=\sqrt{3}$$