1-Calculate-f-x-2-3-if-f-x-y-x-2-y-2-2-Calculate-df-x-y-for-x-1-y-0-dx-1-2-and-dy-1-4-if-f-x-y-x-2-y-2-

Question Number 93478 by Ar Brandon last updated on 13/May/20

$$\mathrm{1}\backslash\mathrm{Calculate}\:\mathrm{f}_{\mathrm{x}} \left(\mathrm{2},\mathrm{3}\right)\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{2}\backslash\mathrm{Calculate}\:\mathrm{df}\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{for}\:\mathrm{x}=\mathrm{1},\:\mathrm{y}=\mathrm{0},\:\mathrm{dx}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{and}\:\mathrm{dy}=\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$

Commented by PRITHWISH SEN 2 last updated on 13/May/20

$$\mathrm{2}.\:\boldsymbol{\mathrm{df}}\left(\boldsymbol{\mathrm{x}},\boldsymbol{\mathrm{y}}\right)=\left(\delta_{\mathrm{x}} \mathrm{f}\right)\mathrm{dx}+\left(\delta_{\mathrm{y}} \mathrm{f}\right)\mathrm{dy}\:=\:\frac{\mathrm{x}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }}\mathrm{dx}+\frac{\mathrm{y}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} }}\mathrm{dy} \\ $$$$=\:\mathrm{1}.\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{0}.\frac{\mathrm{1}}{\mathrm{4}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\mathrm{please}\:\mathrm{check} \\ $$$$ \\ $$

Commented by Ar Brandon last updated on 13/May/20

Thanks ��

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