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Mathematics-Online problems:

Interactive Problem 808: 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)=cos(xy^2). $

Evaluate

$\displaystyle f_x,f_y,f_{xx},f_{yy}$    and $\displaystyle f_{xy} $

at

$\displaystyle P_1=\left(0,\sqrt{\frac\pi 2} \right) , P_2=\left(1,\sqrt{\pi} \right) \ $   and$\displaystyle \ P_3=\left(\frac\pi 2,1\right).$


Solution:

  $ P_1$ $ P_2$ $ P_3$
$ f_x$
$ f_y$ $ \cdot \pi$
$ f_{xx}$ $ \cdot \frac{\pi^2}{4}$ $ \cdot \pi^2$ $ \cdot \pi^2$
$ f_{yy}$ $ \cdot \pi$ $ \cdot \pi$ $ \cdot \pi$
$ f_{xy}$ $ \cdot \pi^{3/2}$

   
(Author: Christian Höfert)

see also:

  automatically generated: 8/11/2017