What is implicit ln(xy^9)=xy ?

The answer to implicit ln(xy^9)=xy is (dy)/(dx)=(xy^2-y)/(x(9-xy))

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implicit ln(xy^9)=xy

implicit derivative

ln (x y^{9}) = x y

\frac{d y}{d x} = \frac{x y ^{2} - y}{x ( 9 - x y )}

Solution steps

ln (x y^{9}) = x y

Treat

y

y (x)

Differentiate both sides:

\frac{y + 9 x \frac{d y}{d x}}{x y} = y + x \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{x y ^{2} - y}{x ( 9 - x y )}

\frac{d y}{d x} = \frac{x y ^{2} - y}{x ( 9 - x y )}

\int \frac{x ^{3}}{27} - \frac{4}{9} x^{2} + \frac{4}{3} x + 1 d x

\frac{d}{d x} (- \frac{3}{x ^{5}})

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

\int_{- 9}^{0} 2 + 81 - x^{2} d x

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

What is implicit ln(xy^9)=xy ?
The answer to implicit ln(xy^9)=xy is (dy)/(dx)=(xy^2-y)/(x(9-xy))