What is implicit x^2-6xy+y^2=6 ?

The answer to implicit x^2-6xy+y^2=6 is (dy)/(dx)=(-x+3y)/(y-3x)

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implicit x^2-6xy+y^2=6

implicit derivative

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

\frac{d y}{d x} = \frac{- x + 3 y}{y - 3 x}

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

2 x - 6 (y + x \frac{d y}{d x}) + 2 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- x + 3 y}{y - 3 x}

\frac{d y}{d x} = \frac{- x + 3 y}{y - 3 x}

f (x) = 2 cos (2 x)

1 + 5 e^{3 t}

\frac{d}{d x} (ln (x^{5}) + 8 ln (x))

f (x) = x^{2} + 6 x - 16, at x = 2

x \to 0 lim (\frac{h ( x )}{g ( x )})

What is implicit x^2-6xy+y^2=6 ?
The answer to implicit x^2-6xy+y^2=6 is (dy)/(dx)=(-x+3y)/(y-3x)