3. Given the function $h(x, y) = x^2 \ln(y) + 3xy^2 + e^x + 5y^3$, find the following:
$\frac{\partial h}{\partial x}$
$\frac{\partial h}{\partial y}$
$\frac{\partial^2 h}{\partial x \partial y}$
4. For the function $f(x, y, z) = xe^y + y^2z + \ln(x) + z^3$, compute:
$\frac{\partial f}{\partial x}$
$\frac{\partial f}{\partial z}$
$\frac{\partial^2 f}{\partial x \partial z}$
5. Given $f(x, y) = \ln(xy) + e^{x+y} + x^2y^3 + 4x$, find the following:
$\frac{\partial f}{\partial x}$
$\frac{\partial f}{\partial y}$
$\frac{\partial^2 f}{\partial x \partial y}$
