What is derivative of x^3+x^2y+7xy^2+y^3=81 ?

The answer to derivative of x^3+x^2y+7xy^2+y^3=81 is (dy)/(dx)=(-3x^2-2xy-7y^2)/(x^2+14xy+3y^2)

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derivative of x^3+x^2y+7xy^2+y^3=81

derivative of

x^{3} + x^{2} y + 7 x y^{2} + y^{3} = 81

\frac{d y}{d x} = \frac{- 3 x ^{2} - 2 x y - 7 y ^{2}}{x ^{2} + 14 x y + 3 y ^{2}}

Solution steps

x^{3} + x^{2} y + 7 x y^{2} + y^{3} = 81

Treat

y

y (x)

Differentiate both sides:

3 x^{2} + 2 x y + \frac{d y}{d x} x^{2} + 7 (y^{2} + 2 x y \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{- 3 x ^{2} - 2 x y - 7 y ^{2}}{x ^{2} + 14 x y + 3 y ^{2}}

\frac{d y}{d x} = \frac{- 3 x ^{2} - 2 x y - 7 y ^{2}}{x ^{2} + 14 x y + 3 y ^{2}}

What is derivative of x^3+x^2y+7xy^2+y^3=81 ?
The answer to derivative of x^3+x^2y+7xy^2+y^3=81 is (dy)/(dx)=(-3x^2-2xy-7y^2)/(x^2+14xy+3y^2)