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Mathematics-Online problems:

Interactive Problem 807: Partial Derivatives

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Let

$\displaystyle f(x,y,z)=x^2z+ye^{x^2z}. $

Evaluate

$\displaystyle f_x,f_y,f_z,f_{xx},f_{yy},f_{zz},f_{xy},f_{xz}$    and $\displaystyle f_{yz} $

at

$\displaystyle P_1=(0,1,ln3) \ $   and$\displaystyle \ P_2=(1,1,ln5).$


Solution:

  $ P_1$ $ P_2$
$ f_x$ $ \cdot ln5$
$ f_y$
$ f_z$
$ f_{xx}$ $ \cdot ln3$ $ \cdot ln5$ + $ \cdot (ln5)^2$
$ f_{yy}$
$ f_{zz}$
$ f_{xy}$ $ \cdot ln5$
$ f_{xz}$ + $ \cdot ln5$
$ f_{yz}$

   
(Author: Christian Höfert)

see also:

  automatically generated: 8/11/2017