Partial derivatives

Exercise

1.: Find the partial derivatives of the followings.
(a): $\displaystyle{z = x^3 + xy^2 + y^3}$
(b): $\displaystyle{z = e^{x} \sin{y}}$
(c): $\displaystyle{z = \log{(x^2 + y^2)}}$
2.: Find the second partial derivatives of the followings.．
(a): $\displaystyle{z = x^3 y + x y^2}$
(b): $\displaystyle{z = x y^2 e^{\frac{x}{y}}}$
(c): $\displaystyle{z = \tan^{-1}{(x^2 + y^2)}}$
3.: Determine whether the function is partial differntiable at the orign．
(a): $\displaystyle{f(x,y) = \left\{\begin{array}{cl} \frac{y^3 - x^2 y}{x^2 + y^2}, & (x,y) \neq (0,0)\\ 0, & (x,y) = (0,0) \end{array}\right.}$
(b): $f(x,y) = \log{(1 + xy + y^2)}$