# Gradient – Calculate maximum direction – Exercise 4265

Exercise

Calculate the direction in which the rate of differentiation of the scalar field

$$u=\ln(x^2+y^2+z^2)$$

At point (1,2,1) it is maximal.

$$\hat{\nabla} u(1,2,1)=\frac{1}{\sqrt{6}}\vec{i}+\frac{2}{\sqrt{6}}\vec{j}+\frac{1}{\sqrt{6}}\vec{k}$$