5. Find the equation of the tangent plane to $x^2 + y^2 + z^2 = 4$ at the point $(1, 1, \sqrt{2})$.
6. Let $f(x, y, z) = 6xy - z^2$, $x = 3r \cos \theta$, $y = \cos^2 \theta$, and $z = 7r$. Use the chain rule to calculate $\frac{\partial f}{\partial \theta}$.
7. Calculate the partial derivative $\frac{\partial w}{\partial z}$ using implicit differentiation of $x^3w + w^4 + wz^2 + 3yz = 0$.
