Use the Chain Rule to calculate the partial derivatives
$g(x,y)=\sin\!\left(x^{2}+y^{2}\right), \quad x=u-3v, y=3u+4v$

$\frac{\partial{g}}{\partial{u}}=$
$\frac{\partial{g}}{\partial{v}}=$
Express your answer in terms of the independent variables $u,v$