What is implicit (dy)/(dx),x^3-3axy+y^3=0 ?

The answer to implicit (dy)/(dx),x^3-3axy+y^3=0 is (dy)/(dx)=(-x^2+ay)/(y^2-ax)

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implicit (dy)/(dx),x^3-3axy+y^3=0

implicit derivative

\frac{d y}{d x}, x^{3} - 3 a x y + y^{3} = 0

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

Solution steps

x^{3} - 3 a x y + y^{3} = 0

Treat

y

y (x)

Differentiate both sides:

3 x^{2} - 3 a (y + x \frac{d y}{d x}) + 3 y^{2} \frac{d y}{d x} = 0

Isolate

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

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

x \to π lim (sin (7 x))

\int_{- 2}^{2} (3 u + 1)^{2} d u

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{3} + 1})

\frac{d}{d x} ((3 x + 7) x^{2})

x \to 2 lim (- x^{4})

What is implicit (dy)/(dx),x^3-3axy+y^3=0 ?
The answer to implicit (dy)/(dx),x^3-3axy+y^3=0 is (dy)/(dx)=(-x^2+ay)/(y^2-ax)