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Math Help - partial derivatives

  1. #1
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    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??
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  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
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    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}<br />
  f(x,y,z) = xe^y \left( {e^{ - z^2 } } \right) \hfill \\<br />
  \frac{{\partial f(x,y,z)}}<br />
{{\partial z}} = xe^y \frac{d}<br />
{{dz}}e^{ - z^2 }  = xe^y ( - 2ze^{ - z^2 } ) =  - 2xze^{y - z^2 }  \hfill \\ <br />
\end{gathered}
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