What is derivative of x^3+y^3=6xy ?

The answer to derivative of x^3+y^3=6xy is (dy)/(dx)=(2y-x^2)/(y^2-2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of x^3+y^3=6xy

derivative

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

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

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}

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