What is implicit (dy)/(dx),x^3+y^3=6xy-1 ?

The answer to implicit (dy)/(dx),x^3+y^3=6xy-1 is (dy)/(dx)=(2y-x^2)/(y^2-2x)

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implicit (dy)/(dx),x^3+y^3=6xy-1

implicit derivative

\frac{d y}{d x}, x^{3} + y^{3} = 6 x y - 1

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

Solution steps

x^{3} + y^{3} = 6 x y - 1

Treat

y

y (x)

Differentiate both sides:

3 x^{2} + 3 y^{2} \frac{d y}{d x} = 6 (x \frac{d y}{d x} + y)

Isolate

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

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

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

\frac{1}{s ( ( s + 2 ) ^{2} + 1 )}

n = 1 \sum \infty 6 e^{- 8 n}

x \to 0 lim (2 - x)

\int - e^{- s t} d t

What is implicit (dy)/(dx),x^3+y^3=6xy-1 ?
The answer to implicit (dy)/(dx),x^3+y^3=6xy-1 is (dy)/(dx)=(2y-x^2)/(y^2-2x)