What is derivative of x^2+y^2x+6x=1 ?

The answer to derivative of x^2+y^2x+6x=1 is (dy)/(dx)=(-2x-y^2-6)/(2xy)

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derivative of x^2+y^2x+6x=1

derivative of

x^{2} + y^{2} x + 6 x = 1

\frac{d y}{d x} = \frac{- 2 x - y ^{2} - 6}{2 x y}

Solution steps

x^{2} + y^{2} x + 6 x = 1

Treat

y

y (x)

Differentiate both sides:

2 x + 2 x y \frac{d y}{d x} + y^{2} + 6 = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 2 x - y ^{2} - 6}{2 x y}

\frac{d y}{d x} = \frac{- 2 x - y ^{2} - 6}{2 x y}

x = \frac{y ^{3}}{3 + y}

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

v = 2 - 4 t - 6 t^{3}

4 y = - 8 x + 2 x + 0

y^{2} = x

What is derivative of x^2+y^2x+6x=1 ?
The answer to derivative of x^2+y^2x+6x=1 is (dy)/(dx)=(-2x-y^2-6)/(2xy)