Question

x^{2} + xy + y^{2} = 100 dy/dx ज्ञात कीजिए

Answer 1

Question :-

$\sf if \: {x}^{2} + xy + {y}^{2} = 100 \: then \: find \: \frac{dy}{dx}$

Answer :-

$\to \boxed{ \sf \frac{dy}{dx} = \frac{ - (2x + y)}{x + 2y} }$

To Find :-

$\to \sf \: \frac{dy}{dx}$

Solution :-

We have ,

$\to \sf {x}^{2} + xy + {y}^{2} = 100 \\ \\ \sf \red{differentiate \: with \: respect \: to \: x} \\ \\ \to \sf \frac{d}{dx} {x}^{2} + \frac{d}{dx} xy + \frac{d}{dx} {y}^{2} = \frac{d}{dx} 100 \\ \\ \tt we \: know \: that \\ \\ \boxed{ \sf \frac{d}{dx} \:(constant \: ) = 0} \\ \\ \boxed{ \sf \frac{d}{dx} {x}^{n - 1} = n {x}^{n - 1} } \\ \\ \sf for \: product \: of \: two \: function \: we \: wil \: use \: \\ \sf \: chain \: rule \: of \: differentiation \: \\ \sf \: that \: \:is - \\ \boxed{ \sf \frac{d}{dx} \: xy \: = x \frac{d}{dx} y + y \frac{d}{dx} x \: } \\ \sf hence \\ \\ \to \sf \: 2x + x \frac{dy}{dx} + y \: + 2y \frac{dy}{dx} = 0 \\ \\ \to \sf \: \frac{dy}{dx} \big\{x + 2y \big \} = - y - 2x \\ \\ \to \boxed{ \sf \frac{dy}{dx} = \frac{ - (2x + y)}{x + 2y} }$

Answer 2

dy/dx =  -(2x + y)/(x + 2y) , यदि x²  + xy  + y²  = 100

Step-by-step explanation:

dy/dx ज्ञात कीजिए

x²  + xy  + y²  = 100

=> 2x  + xdy/dx  + y  + 2ydy/dx  = 0

=> (dy/dx)(x+ 2y) + 2x + y = 0

=> dy/dx =  -(2x + y)/(x + 2y)

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