How do you find the derivative of #xe^y=y-1#?

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Answer 1 · 2015-02-19T23:49:22

Use implicit differentiation. On the left hand side use the product rule.

We are differentiating with respect to x

#e^y+xe^ydy/dx=dy/dx #

get everything with #dy/dx# on one side of the equation

#xe^ydy/dx-dy/dx=-e^y#

Factor left hand side

#dy/dx(xe^y-1)=-e^y #

now divide both sides by #xe^y-1 #

#dy/dx=-e^y/(xe^y-1) #