Compute $f_x$, $\frac{\partial f}{\partial y}$, $\vec \nabla f$, and $df$ for each of the following.
- $f(x,y) = x^2y$
- $f(x,y) = 3xy+4y^2$
- $f(x,y) = \sin(xy^2)$
For each function below, construct a (1) contour plot and (2) 3D surface plot.
- $f(x,y)=y-x^2$
- $f(x,y)=4-x^2$
- $f(x,y)=4-|y|$
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