Exercises
[1FX]Check that the following partial derivatives exist, and compute them:
\begin{align*} \frac{\partial ~ }{\partial {x}} {\Big( 4xy + 3x^ 2 y -z y^ 2 \Big)}~ ~ & ,~ ~ \frac{\partial ~ }{\partial {y}} \Big( 4xy + 3x^ 2 y -z y^ 2 \Big)\\ \frac{\partial ~ }{\partial {x}} { \frac{ze^{x+|y|}}{1+x^ 2|y|} }~ ~ & ,~ ~ \frac{\partial ~ }{\partial {z}} \frac{ze^{x+|y|}}{1+x^ 2|y|} \end{align*}Solution 1