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

The answer to implicit (dy)/(dx),x^2+y^2=(2x^2+4y^2-x)2 is (dy)/(dx)=-(3x-1)/(7y)

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

implicit derivative

\frac{d y}{d x}, x^{2} + y^{2} = (2 x^{2} + 4 y^{2} - x) 2

\frac{d y}{d x} = - \frac{3 x - 1}{7 y}

Solution steps

x^{2} + y^{2} = (2 x^{2} + 4 y^{2} - x) \cdot 2

Treat

y

y (x)

Differentiate both sides:

2 x + 2 y \frac{d y}{d x} = 2 (4 x + 8 y \frac{d y}{d x} - 1)

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{3 x - 1}{7 y}

\frac{d y}{d x} = - \frac{3 x - 1}{7 y}

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

\int 2 cos (2 x - 5) d x

x \to 42 lim (\frac{x ^{2}}{7} - \frac{6}{x})

\frac{d}{d x} ((ln (2 x))^{3})

\int_{0}^{\frac{7}{6}} 7 x - 6 x^{2} d x

What is implicit (dy)/(dx),x^2+y^2=(2x^2+4y^2-x)2 ?
The answer to implicit (dy)/(dx),x^2+y^2=(2x^2+4y^2-x)2 is (dy)/(dx)=-(3x-1)/(7y)