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

find    (dy/dx) if   x^2 +y^2 =4

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

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

y=±(√(4−x^2 ))  2x+2y(dy/dx)=0 ⇒ (dy/dx)=−(x/y)  (dy/dx)=∓(x/( (√(4−x^2 ))))

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

Answered by Adel last updated on 18/Jan/21

2x+2y(dy/dx)=0⇒(dy/dx)=−(x/y)  danish

$$\mathrm{2x}+\mathrm{2y}\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{0}\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}=−\frac{\mathrm{x}}{\mathrm{y}} \\ $$$$\boldsymbol{{danish}} \\ $$

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