Let $f(z,t) = 5 z \ln{\left (z \right )}$. Calculate the partial derivatives of $f$.
$\displaystyle \pdiff{ f }{ z } = $
$\displaystyle \pdiff{ f }{ t } = $
Let $g(s,t) = 8 s^{2} t^{2} + 9 s^{2} + 9 s t^{2}$. Calculate the partial derivatives of $g$.
$\displaystyle \pdiff{ g }{ s } = $
$\displaystyle \pdiff{ g }{ t } = $
Let $f(z,y) = 3 e^{8 y + 7 z}$. Calculate the partial derivatives of $f$.
$\displaystyle \pdiff{ f }{ y } = $
Let $g(t,y) = \left(- 10 y - 10\right) \ln{\left (t + 3 \right )}$. Calculate the partial derivatives of $g$.
$\displaystyle \pdiff{ g }{ y } = $
Let $f(z,y) = y e^{8 z^{2}}$. Calculate the partial derivatives of $f$.
Let $g(t,s) = 8 e^{9 s} + 10 e^{- 8 t}$. Calculate the partial derivatives of $g$.