What is derivative of x+y-x^3y=15 ?

The answer to derivative of x+y-x^3y=15 is (dy)/(dx)=(3x^2y-1)/(1-x^3)

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derivative of x+y-x^3y=15

derivative of

x + y - x^{3} y = 15

\frac{d y}{d x} = \frac{3 x ^{2} y - 1}{1 - x ^{3}}

Solution steps

x + y - x^{3} y = 15

Treat

y

y (x)

Differentiate both sides:

1 + \frac{d y}{d x} - 3 x^{2} y - x^{3} \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{3 x ^{2} y - 1}{1 - x ^{3}}

\frac{d y}{d x} = \frac{3 x ^{2} y - 1}{1 - x ^{3}}

x = (1 - y^{2})^{\frac{1}{2}}

2 x^{2} + 2 y - 2 x y = 4

x^{2} + 2 x y = y^{2}

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

y - 4 = 2 (x - 1)^{2}

What is derivative of x+y-x^3y=15 ?
The answer to derivative of x+y-x^3y=15 is (dy)/(dx)=(3x^2y-1)/(1-x^3)