How do you differentiate e^(xy)+x^2-y^2=0

June Mejia

June Mejia

Answered question

2022-08-11

How do you differentiate e x y + x 2 - y 2 = 0

Answer & Explanation

Irene Simon

Irene Simon

Beginner2022-08-12Added 16 answers

You have an Implicit Function in which y is function of x so you have to derive it as well.
You get:
e x y ( 1 y + x d y d x ) + 2 x - 2 y d y d x = 0
where you used the Product Rule for the exponent of e;
y e x y + x e x y d y d x + 2 x - 2 y d y d x = 0
d y d x [ x e x y - 2 y ] = - 2 x - y e x y
finally:
d y d x = - 2 x + 2 y e x y x e x y - 2 y

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