What is implicit (dy)/(dx),ln(xy^3)=xy ?

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

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implicit (dy)/(dx),ln(xy^3)=xy

implicit derivative

\frac{d y}{d x}, ln (x y^{3}) = x y

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

Solution steps

ln (x y^{3}) = x y

Treat

y

y (x)

Differentiate both sides:

\frac{y + 3 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 ( 3 - x y )}

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

\int \frac{tan ^{3} ( ln ( x ) )}{2 x} d x

f (x) = cos^{5} (x)

arcsec (\frac{1}{4 t ^{5}})

n = 0 \sum \infty \frac{z ^{n}}{n ^{2}}

\int 2 x^{13} e^{- x^{7}} d x

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