pochodne 2 rzedu zadanko
: 12 wrz 2007, o 10:42
\(\displaystyle{ f(x,y)=}\)\(\displaystyle{ x^{4}}\)\(\displaystyle{ y^{3}+}\)\(\displaystyle{ x^{3}}\)\(\displaystyle{ y^{3}}\)
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\(\displaystyle{ \frac{\partial f}{\partial x} = 4x^3y^3+3x^2y^3 \\
\frac{\partial f}{\partial y} = 3x^4y^2+3x^3y^2 \\
\frac{\partial^2 f}{\partial x^2} = 12x^2y^3+6xy^3 \\
\frac{\partial^2 f}{\partial y^2} = 6x^4y+6x^3y \\
\frac{\partial^2 f}{\partial x y} = 12x^3y^2+9x^2y^2}\)