Question

Find \frac{dy}{dx} using implicit differentiation xe^{y}=x-y

Differential equations
ANSWERED
asked 2021-06-07
Find \(\frac{dy}{dx}\) using implicit differentiation \(xe^{y}=x-y\)

Answers (1)

2021-06-08
Step 1
\(xe^{y}=x-y\)
\(\Rightarrow\) Implicit diff
\(e^{y}+xe^{y}\frac{dy}{dx}=1-\frac{dy}{dx}\)
\(\Rightarrow xe^{y}\frac{dy}{dx}+\frac{dy}{dx}=1-e^{y}\)
\(\Rightarrow(xe^{y}+1)\frac{dy}{dx}=(1-e^{y})\)
\(\Rightarrow\frac{dy}{dx}=\frac{1-e^{y}}{xe^{y}+1}\)
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