What is implicit xy+5e^y=5e ?

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

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implicit xy+5e^y=5e

implicit derivative

x y + 5 e^{y} = 5 e

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

Solution steps

x y + 5 e^{y} = 5 e

Treat

y

y (x)

Differentiate both sides:

y + x \frac{d y}{d x} + e^{y} \frac{d y}{d x} = 0

Isolate

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

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

\frac{d}{d x} (tan (a x + b))

\frac{\partial}{\partial x} (3 y^{2} x - y^{3} - x^{4})

x^{2} y^{^{''}} = y^{^{'}} + (y^{^{'}})^{2}

\frac{\partial}{\partial x} (x^{x y})

\int \frac{1}{x ^{4} - 16} d x

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