What is implicit (dy)/(dx),xy-5y^2=6 ?

The answer to implicit (dy)/(dx),xy-5y^2=6 is (dy)/(dx)=-y/(x-10y)

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implicit (dy)/(dx),xy-5y^2=6

implicit derivative

\frac{d y}{d x}, x y - 5 y^{2} = 6

\frac{d y}{d x} = - \frac{y}{x - 10 y}

Solution steps

x y - 5 y^{2} = 6

Treat

y

y (x)

Differentiate both sides:

y + x \frac{d y}{d x} - 10 y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y}{x - 10 y}

\frac{d y}{d x} = - \frac{y}{x - 10 y}

\int x^{5} 4 + x^{6} d x

\int \frac{x ^{2}}{x ^{2} - 6 x + 10} d x

x \to 0 + lim (\frac{1}{5 x})

y = x^{3} - 2 x + 1, y = - 2 x, x = 1

x \to 1 lim ([x])

What is implicit (dy)/(dx),xy-5y^2=6 ?
The answer to implicit (dy)/(dx),xy-5y^2=6 is (dy)/(dx)=-y/(x-10y)