What is implicit (dy)/(dx),e^y=x+y ?

The answer to implicit (dy)/(dx),e^y=x+y is (dy)/(dx)= 1/(e^y-1)

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implicit (dy)/(dx),e^y=x+y

implicit derivative

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

\frac{d y}{d x} = \frac{1}{e ^{y} - 1}

Solution steps

e^{y} = x + y

Treat

y

y (x)

Differentiate both sides:

e^{y} \frac{d y}{d x} = 1 + \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{e ^{y} - 1}

\frac{d y}{d x} = \frac{1}{e ^{y} - 1}

0.4 x - 1.295, - 1.4206, - 1.486

n = 2 \sum \infty (- 0.75)^{n}

\frac{1}{x ^{2}} 0

x \to - \infty lim (2^{x} + 1)

\int \frac{e ^{5 x} + 5 e ^{x} + 7}{e ^{x}} d x

What is implicit (dy)/(dx),e^y=x+y ?
The answer to implicit (dy)/(dx),e^y=x+y is (dy)/(dx)= 1/(e^y-1)