Key to "Find dydx using implicit differentiation xey=x−y"

babeeb0oL

Answered question

2021-06-07

Find

\frac{d y}{d x}

using implicit differentiation

x e^{y} = x - y

2abehn

Skilled2021-06-08Added 88 answers

Step 1

x e^{y} = x - y

\Rightarrow

Implicit diff

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

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

\Rightarrow (x e^{y} + 1) \frac{d y}{d x} = (1 - e^{y})

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

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