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

Sydney Stein

Sydney Stein

Open question

2022-08-16

How do you find the derivative of x e y = y - 1

Answer & Explanation

Howard Robertson

Howard Robertson

Beginner2022-08-17Added 6 answers

Use implicit differentiation. On the left hand side use the product rule.
We are differentiating with respect to x
e y + x e y d y d x = d y d x
get everything with d y d x on one side of the equation
x e y d y d x - d y d x = - e y
Factor left hand side
d y d x ( x e y - 1 ) = - e y
now divide both sides by x e y - 1
d y d x = - e y x e y - 1

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