What is derivative of x^2y+y^2x=6 ?

The answer to derivative of x^2y+y^2x=6 is (dy)/(dx)=(-2xy-y^2)/(x(x+2y))

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derivative of x^2y+y^2x=6

derivative of

x^{2} y + y^{2} x = 6

\frac{d y}{d x} = \frac{- 2 x y - y ^{2}}{x ( x + 2 y )}

Solution steps

x^{2} y + y^{2} x = 6

Treat

y

y (x)

Differentiate both sides:

2 x y + \frac{d y}{d x} x^{2} + 2 x y \frac{d y}{d x} + y^{2} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 2 x y - y ^{2}}{x ( x + 2 y )}

\frac{d y}{d x} = \frac{- 2 x y - y ^{2}}{x ( x + 2 y )}

What is derivative of x^2y+y^2x=6 ?
The answer to derivative of x^2y+y^2x=6 is (dy)/(dx)=(-2xy-y^2)/(x(x+2y))