What is implicit x^3+y^3=8xy-5 ?

The answer to implicit x^3+y^3=8xy-5 is (dy)/(dx)=(8y-3x^2)/(3y^2-8x)

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implicit x^3+y^3=8xy-5

implicit derivative

x^{3} + y^{3} = 8 x y - 5

\frac{d y}{d x} = \frac{8 y - 3 x ^{2}}{3 y ^{2} - 8 x}

Solution steps

x^{3} + y^{3} = 8 x y - 5

Treat

y

y (x)

Differentiate both sides:

3 x^{2} + 3 y^{2} \frac{d y}{d x} = 8 (x \frac{d y}{d x} + y)

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{8 y - 3 x ^{2}}{3 y ^{2} - 8 x}

\frac{d y}{d x} = \frac{8 y - 3 x ^{2}}{3 y ^{2} - 8 x}

\frac{\partial}{\partial y} (\frac{x y}{5 x + 3 y})

2 x e^{x} csc (x)

\int \frac{t}{2 y ^{4}} d t

\int \frac{( 7 x - 4 ) ( 3 x + 5 ) ^{2}}{x ^{2}} d x

\frac{\partial ^{2}}{\partial y ^{2}} (\frac{x}{x ^{2} + y ^{2}})

What is implicit x^3+y^3=8xy-5 ?
The answer to implicit x^3+y^3=8xy-5 is (dy)/(dx)=(8y-3x^2)/(3y^2-8x)