Wyznaczyc ekstrema lokalne
: 29 sty 2008, o 16:45
\(\displaystyle{ f(x,y)=xe^{y ^{2}- x^{2}}=e^{lnx}\cdot e^{y^2-x^2}=e^{lnx+y^2-x^2} \\
\frac{\partial f}{\partial x}=
e^{lnx+y^2-x^2}\cdot (lnx+y^2-x^2)'_x=
e^{lnx+y^2-x^2}\cdot (\frac{1}{x}-2x)\\
\frac{\partial f}{\partial y}=
e^{lnx+y^2-x^2}\cdot (lnx+y^2-x^2)'_y=
e^{lnx+y^2-x^2}\cdot (2y)}\)
\frac{\partial f}{\partial x}=
e^{lnx+y^2-x^2}\cdot (lnx+y^2-x^2)'_x=
e^{lnx+y^2-x^2}\cdot (\frac{1}{x}-2x)\\
\frac{\partial f}{\partial y}=
e^{lnx+y^2-x^2}\cdot (lnx+y^2-x^2)'_y=
e^{lnx+y^2-x^2}\cdot (2y)}\)