$5(10$ pts$)$

$5$pts $($a$)$ Find the directional derivative of the function $f(x,y)=4xy-x^2-y^2$ in the direction of vector $v=($:$-3,2$:$)$ at the point $P(\frac{1}{3},\frac{2}{3}).$

$5$pts $($b$)$ Find the direction vector $u$ which gives the maximum value for $D_{u}f$ at the point $P(\frac{1}{3},\frac{2}{3}),$ and compute that maximum value.