Let $f(x,s) = - 6 e^{9 s - x}$. Calculate the partial derivatives of $f$.
$\displaystyle \pdiff{ f }{ x } = $
$\displaystyle \pdiff{ f }{ s } = $
Let $f(x,t) = 5 x \ln{\left (x \right )}$. Calculate the partial derivatives of $f$.
$\displaystyle \pdiff{ f }{ t } = $
Let $g(y,s) = \left(- s - 9\right) \ln{\left (y + 2 \right )}$. Calculate the partial derivatives of $g$.
$\displaystyle \pdiff{ g }{ y } = $
$\displaystyle \pdiff{ g }{ s } = $
Let $f(s,y) = 2 s^{2} y + 2 s - 5 y^{2}$. Calculate the partial derivatives of $f$.
$\displaystyle \pdiff{ f }{ y } = $
Let $f(x,z) = 10 z^{3} e^{- 7 x^{3}}$. Calculate the partial derivatives of $f$.
$\displaystyle \pdiff{ f }{ z } = $
Let $f(z,y) = - 4 e^{3 y} + 8 e^{2 z}$. Calculate the partial derivatives of $f$.