2. Let $g(x, y) = \sin \pi(2x - y)$; $P(-1, -1)$; $(rac{5}{13}, rac{-12}{13})$. Compute the directional derivative at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector.
#2 is left for the student to complete and to turn in
Note: A unit vector $\vec{u}$ is a vector with length equal to 1
Length of $\vec{u} = <a, b>$: $|\vec{u}| = \sqrt{a^2 + b^2}$
The directional derivative of f in the direction of $\vec{u}$ is
$D_\vec{u} f(a, b) = \nabla f(a, b) \cdot \vec{u}$
$= <f_x(a, b), f_y(a, b)> \cdot <u_1, u_2>$, where $\vec{u} = <u_1, u_2>$
$= f_x(a, b)u_1 + f_y(a, b)u_2$