Answer
a) See the explanation below.
b) See the explanation below.
Work Step by Step
a) The directional derivatives of $f$ at $(x_0,y_0)$ in the direction of a unit vector $\over{u}$ can be expressed as:
$D_uf(x_0,y_0)=\lim\limits_{n \to 0}\dfrac{f(x_0+na,y_0+nb)-f(x_0,y_0)}{l}$
The interpretation of the directional derivative can be defined as the rate of change of $f$ at $(x_0,y_0)$ in the direction of a unit vector $\over{u}$.
b) The expression for $D_uf(x_0,y_0)$ in terms of the first partial derivatives of $f$ that is, $f_x,f_y$ is:
$D_uf(x_0,y_0)=f_x(x_0,y_0)a+f_y(x_0,y_0)b$
