What is implicit ln(x^2+y)-xy^2=10 ?

The answer to implicit ln(x^2+y)-xy^2=10 is (dy)/(dx)=(x^2y^2+y^3-2x)/(1-2x^3y-2xy^2)

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implicit ln(x^2+y)-xy^2=10

implicit derivative

ln (x^{2} + y) - x y^{2} = 10

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

Solution steps

ln (x^{2} + y) - x y^{2} = 10

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\frac{cos ( x )}{1 + a \cdot sin ( x )}

\int 14 e^{- 14 x} d x

\int x^{3} - \frac{1}{2} x^{2} + 4 d x

f (x) = e^{x} (x^{4} + 3), (0, 3)

\frac{d}{d x} (\frac{x ^{2} - 10 x + 9}{( x - 5 ) ^{2}})

What is implicit ln(x^2+y)-xy^2=10 ?
The answer to implicit ln(x^2+y)-xy^2=10 is (dy)/(dx)=(x^2y^2+y^3-2x)/(1-2x^3y-2xy^2)