Question

differentiate x²+y²-5=0 w.r.to x

Answer 1

SOLUTION

TO DETERMINE

To Differentiate x² + y² - 5 = 0 with respect to x

EVALUATION

Here it is given that

$\sf{ {x}^{2} + {y}^{2} - 5 = 0}$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ \frac{d}{dx} ( {x}^{2} + {y}^{2} - 5) = \frac{d}{dx} (0)}$

$\displaystyle \sf{ \implies \: \frac{d}{dx} ( {x}^{2} ) + \frac{d}{dx}( {y}^{2} ) -\frac{d}{dx}( 5) = \frac{d}{dx} (0)}$

$\displaystyle \sf{ \implies \: 2 {x}^{2 - 1} +2 {y}^{2 - 1} \frac{dy}{dx} -0 = 0}$

$\displaystyle \sf{ \implies \: 2 x +2y \frac{dy}{dx} = 0}$

$\displaystyle \sf{ \implies \: x +y \frac{dy}{dx} = 0}$

$\displaystyle \sf{ \implies \: y \frac{dy}{dx} = - x}$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = - \frac{x}{y} }$

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