How do you differentiate x^2+y^2=2xy

Expositur3e

Expositur3e

Open question

2022-08-20

How do you differentiate x 2 + y 2 = 2 x y

Answer & Explanation

Mohammad Hampton

Mohammad Hampton

Beginner2022-08-21Added 7 answers

Explanation:
For x 2 + y 2 = 2 x y , we get (by differentiating implicitly), d y d x = 1
That's the same as the derivative of a linear function with slope, 1. Hmmmmm. Let's see:
If we have x 2 + y 2 = 2 x y
The we must also have: x 2 - 2 x y + y 2 = 0
Factoring gets us: ( x - y ) 2 = 0
And the only way for that to happen is to have: x - y = 0
So y = x
and d y d x = 1
(Which we already knew by differentiating, but this may be of interest as well.)

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