What is implicit ln(5+e^{xy})=y ?

The answer to implicit ln(5+e^{xy})=y is (dy)/(dx)=-(e^{xy}y)/(e^{xy)x-5-e^{xy}}

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implicit ln(5+e^{xy})=y

implicit derivative

ln (5 + e^{x y}) = y

\frac{d y}{d x} = - \frac{e ^{x y} y}{e ^{x y} x - 5 - e ^{x y}}

Solution steps

ln (5 + e^{x y}) = y

Treat

y

y (x)

Differentiate both sides:

\frac{e ^{x y} ( x \frac{d y}{d x} + y )}{5 + e ^{x y}} = \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{e ^{x y} y}{e ^{x y} x - 5 - e ^{x y}}

\frac{d y}{d x} = - \frac{e ^{x y} y}{e ^{x y} x - 5 - e ^{x y}}

\frac{\partial}{\partial x} (ln (2 x + 2 c t))

\int \frac{9 ( csc ( t ) ) ^{2}}{cot ( t )} d t

x \to 0 lim (x^{5} - 6 x^{4} + 7)

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

\frac{d}{d x} (x \cdot arctan (x))

What is implicit ln(5+e^{xy})=y ?
The answer to implicit ln(5+e^{xy})=y is (dy)/(dx)=-(e^{xy}y)/(e^{xy)x-5-e^{xy}}