3. Find the rate of change of $f(x, y, z) = xy^2z^3$ at $P = (1, -1, -1)$ in the direction of $v = (2, 1, 1)$.
4. Let $f(x, y)$ be a function of two variables.
(a) Calculate $\frac{\partial f}{\partial u}$ and $\frac{\partial f}{\partial v}$ in terms of $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$, where $x = uv$ and $y = u + v$.
(b) Show that $u\frac{\partial f}{\partial u} - v\frac{\partial f}{\partial v} = (u - v)\frac{\partial f}{\partial y}$, where $x = uv$ and $y = u + v$.
