Use the chain rule to find $\frac{dz}{dt}$, where $$z = x^2 y + x y^2,\quad x = 5 + t^4,\quad y = 5 - t^6$$
First the pieces:

$\frac{\partial z}{\partial x} =$
$\frac{\partial z}{\partial y} =$
$\frac{dx}{dt} =$
$\frac{dy}{dt} =$

End result (in terms of just $t$):
$\frac{dz}{dt} =$