Exercises

01

Linearities of directional derivative

• (a) Show that $D_{\mathbf{v}}(\lambda f+g)=\lambda \cdot D_{\mathbf{v}}f+D_{\mathbf{v}}g$.
• (b) Show that $D_{\lambda \cdot \mathbf{v}}f=\lambda \cdot D_{\mathbf{v}}f$.

02

Directional derivative

Suppose $f(x,y,z)=10+y{z}^2+x^{2}z-x{y}^2$. Find the rate of change of $f$ at the point $(1,2,1)$ in the direction of the vector $(0,1,1)$.