Calculate the directional derivative of $f(x,y)=\sin^{-1}\!\left(xy\right)$ in the direction of $\mathbf{v}=3 \mathbf{i}+5\mathbf{j}$ at the point $P=(0.5,0.5)$. Remember to normalize the direction vector.

$D_uf(0.5,0.5)=$