Math, asked by arshdeepbajwa3238, 9 months ago

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

Answers

Answered by Sharad001
19

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} }

Answered by amitnrw
0

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)

और अधिक जानें :

sin(x²+5)"

brainly.in/question/15286193

sin (ax+b) फलन का अवकलन कीजिए

brainly.in/question/15286166

Similar questions