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Question Number 129727 by abdurehime last updated on 18/Jan/21

$$\mathrm{find}\frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{if}{\mathrm{x}}^2+{\mathrm{y}}^2=4$$

Answered by Ar Brandon last updated on 18/Jan/21

$$\mathrm{y}=\pm \sqrt{4-{\mathrm{x}}^2}$$$$2\mathrm{x}+2\mathrm{y}\frac{\mathrm{dy}}{\mathrm{dx}}=0\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{\mathrm{x}}{\mathrm{y}}$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\mp \frac{\mathrm{x}}{\sqrt{4-{\mathrm{x}}^2}}$$

Answered by Adel last updated on 18/Jan/21

$$2\mathrm{x}+2\mathrm{y}\frac{\mathrm{dy}}{\mathrm{dx}}=0\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{\mathrm{x}}{\mathrm{y}}$$$$\mathit{d}\mathit{a}\mathit{n}\mathit{i}\mathit{s}\mathit{h}$$

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