1. ## partial derivatives

1. what would be the derivative of : xe^[y-(z^2)]
when Z is the variable?

2. use differentials to estimate the amount of metal in a closed cylindrical can that is 10cm high and 4 cm in the diametre if the metal in the top and bottom is 0.1 cm thick and the metal in the sides is 0.05 cm thick.

how do i do this??

2. what exactly don't you understand?, if you know the definition of partial derivative and the derivative of the e^x function there's no reason for a problem.

$\begin{gathered}
f(x,y,z) = xe^y \left( {e^{ - z^2 } } \right) \hfill \\
\frac{{\partial f(x,y,z)}}
{{\partial z}} = xe^y \frac{d}
{{dz}}e^{ - z^2 } = xe^y ( - 2ze^{ - z^2 } ) = - 2xze^{y - z^2 } \hfill \\
\end{gathered}$