Compute the directional derivative of the following function at the given point $P$ in the direction of the given vector. Be sure to use a unit vector for the direction vector.

$f(x,y)=ln(3+x^2+y^2)$;$P(2,-2)$;$($:$3,3$:$)$

Find the gradient of $f(x,y)=ln(3+x^2+y^2).$

gradf$(x,y)=|\frac{2x}{3+x^2+y^2},\frac{2y}{3+x^2+y^2}|$

The directional derivative is

$($Type an exact answer, using radicals as needed.$)$