4. Find the tangent plane to the surface given by the equation $z = x \sin(xy)$ at the point $(2, 4, 4)$.
5. Find $\frac{\partial z}{\partial t}$ for the function $z = x^2y + x^2y^2$ where $x = e^t$ and $y = e^t$.
6. Find $\frac{dy}{dx}$ for the equation $x^2 + y^2 + x^2y^2 = x^2$.
7. Find the derivative of the function $f(x, y, z) = \frac{1}{x} \ln(y)e^{-xyz}$ in the direction of the unit vector $\vec{u} = \frac{1}{\sqrt{3}} <1, 1, 1>$.
