Problem 1.1.4. (i) Let $f(x, y, z) = xy + xy^2 - \ln(xyz)$. \\
compute the partial derivatives $f_x, f_y, f_z, f_{xy}, f_{xz}$ and $f_{xx}$.
Solution:
(ii) Let $g(x, y) = xe^y$, compute $g_{xx}(1, 0), g_{xy}(1, 0)$ and $g_{yy}(1, 0)$
Solution:
(iii) Let
$f(x, y, u, v) = \frac{x^2 + e^{x^2}}{3y^2 + \ln(2 + v^2)}$
What is the fastest way to show that $f_{uvxy}(x, y, u, v) = 0$ for all $(x, y, u, v)$?
Solution
