What is implicit (dy)/(dx),x^2y+xy^2=6 ?

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

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implicit (dy)/(dx),x^2y+xy^2=6

implicit derivative

\frac{d y}{d x}, x^{2} y + x y^{2} = 6

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

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

\int \frac{1}{3 - 4 x} d x

\frac{d}{d x} (\frac{x}{9.8})

f (x) = (ln (7)) e^{x}

f (x) = \frac{1}{x ^{3}}, (- 2, - \frac{1}{8})

\int x e^{\frac{x}{3}} d x

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