What is implicit (dy)/(dx),x^2+5x+9xy-y^2=4 ?

The answer to implicit (dy)/(dx),x^2+5x+9xy-y^2=4 is (dy)/(dx)=(-2x-5-9y)/(9x-2y)

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implicit (dy)/(dx),x^2+5x+9xy-y^2=4

implicit derivative

\frac{d y}{d x}, x^{2} + 5 x + 9 x y - y^{2} = 4

\frac{d y}{d x} = \frac{- 2 x - 5 - 9 y}{9 x - 2 y}

Solution steps

x^{2} + 5 x + 9 x y - y^{2} = 4

Treat

y

y (x)

Differentiate both sides:

2 x + 5 + 9 (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{- 2 x - 5 - 9 y}{9 x - 2 y}

\frac{d y}{d x} = \frac{- 2 x - 5 - 9 y}{9 x - 2 y}

1 + 6 x^{\frac{3}{2}}

\int \frac{1}{3 + x + 2} d x

y^{^{''}} - 2 y^{^{'}} - 3 y = 64 x e^{- x}

\int_{0}^{a} (\frac{m}{2 π ( a - x )})^{5} d x

y = 3 x^{4} - 3 x^{2}, y = 3 x^{2}

What is implicit (dy)/(dx),x^2+5x+9xy-y^2=4 ?
The answer to implicit (dy)/(dx),x^2+5x+9xy-y^2=4 is (dy)/(dx)=(-2x-5-9y)/(9x-2y)