pochodne cząstkowe f(x,y)

[praktyk]

do sprawdzenia:
1.
\(\displaystyle{ f(x,y)=(x-1)^2-2y^2}\)
\(\displaystyle{ f'x=2x-2}\)
\(\displaystyle{ f'y=-4y}\)
\(\displaystyle{ f'xx=2}\)
\(\displaystyle{ f'yy=-4}\)
\(\displaystyle{ f'xy=0}\)
\(\displaystyle{ f'yx=0}\)

2.
\(\displaystyle{ f(x,y)=xlny}\)
\(\displaystyle{ f'x=lny}\)
\(\displaystyle{ f'y= \frac{x}{y}}\)
\(\displaystyle{ f'xx=0}\)
\(\displaystyle{ f'yy= -\frac{x}{y^2}}\)
\(\displaystyle{ f'xy= \frac{1}{y}}\)
\(\displaystyle{ f'yx= \frac{1}{y}}\)

[miki999]

Polecam:
http://wims.unice.fr/wims/wims.cgi?sess ... unction.en

http://www.wolframalpha.com/


1. \(\displaystyle{ f'x,\ f'xx}\)- źle.

[praktyk]

\(\displaystyle{ f'x=2x-2}\)
\(\displaystyle{ f'xx=2}\)

[miodzio1988]

Polecam

http://www.wolframalpha.com/

teraz ok jest