What is implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0 ?

The answer to implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0 is (dy)/(dx)=(-12x-3y)/(4y+17+3x)

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implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0

implicit derivative

\frac{d y}{d x}, 6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0

\frac{d y}{d x} = \frac{- 12 x - 3 y}{4 y + 17 + 3 x}

Solution steps

6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0

Treat

y

y (x)

Differentiate both sides:

12 x + 4 y \frac{d y}{d x} + 17 \frac{d y}{d x} + 3 (x \frac{d y}{d x} + y) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 12 x - 3 y}{4 y + 17 + 3 x}

\frac{d y}{d x} = \frac{- 12 x - 3 y}{4 y + 17 + 3 x}

y^{^{''}} - 7 y^{^{'}} + 12 y = 0

2 x + 1

y^{^{''}} - 3 y^{^{'}} + 18 y = 0

\int (x - 2) (x - 3)^{6} d x

\frac{\partial}{\partial x} (4 (x - y) e^{4 y + 2 x^{2}})

What is implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0 ?
The answer to implicit (dy)/(dx),6x^2+3xy+2y^2+17y-6=0 is (dy)/(dx)=(-12x-3y)/(4y+17+3x)