Question

xy(x+y)=2 then dy/dx=? PLEASE SOLVE IT FRIENDS

Answer 1

hello friend..!!

to find dy/dx in the above question,

it is given that ,  xy( x + y ) = 2

⇒ x²y  + y²x = 2 

⇒ $\frac{d}{dx}$ (x²y) + $\frac{d}{dx}$(xy²) = $\frac{d}{dx}$(2)

⇒ x²$\frac{dy}{dx}$ + 2xy + 2xy$\frac{dy}{dx}$ + y² = 0 

⇒ x² $\frac{dy}{dx}$ + 2xy$\frac{dy}{dx}$ + 2xy + y² = 0 

⇒ $\frac{dy}{dx}$ ( x² + 2xy )  = - ( 2xy + y² )

⇒ $\frac{dy}{dx}$ = - ( 2xy + y² ) / x² + 2xy .

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hope it is useful...!!