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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}

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)