Question Number 130884 by LYKA last updated on 30/Jan/21
![let f(x.y)=[x^2 +xy,x^2 −y^2 ] prove from defination of derivative that : Df_((x,y)) (1,2)=[4x+y,−2x+4y]](https://www.tinkutara.com/question/Q130884.png)
$${let}\:{f}\left({x}.{y}\right)=\left[{x}^{\mathrm{2}} +{xy},{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right]\: \\ $$$$ \\ $$$${prove}\:{from}\:{defination}\:{of}\: \\ $$$${derivative}\:{that}\:: \\ $$$${Df}_{\left({x},{y}\right)} \left(\mathrm{1},\mathrm{2}\right)=\left[\mathrm{4}\boldsymbol{{x}}+\boldsymbol{{y}},−\mathrm{2}{x}+\mathrm{4}{y}\right] \\ $$$$ \\ $$
Commented by LYKA last updated on 30/Jan/21
$${okay}\:{sir} \\ $$