Resolved: "How do you differentiate e x y +..."

June Mejia

Answered question

2022-08-11

How do you differentiate

e^{x y} + x^{2} - y^{2} = 0

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} \cdot (1 \cdot y + x \frac{d y}{d x}) + 2 x - 2 y \frac{d y}{d x} = 0

where you used the Product Rule for the exponent of e;

y e^{x y} + x e^{x y} \frac{d y}{d x} + 2 x - 2 y \frac{d y}{d x} = 0

\frac{d y}{d x} [x e^{x y} - 2 y] = - 2 x - y e^{x y}

finally:

\frac{d y}{d x} = - \frac{2 x + 2 y e^{x y}}{x e^{x y} - 2 y}

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