Find dy/dx by implicit differentiation x^2-4xy+y^2=4

rkus2zg0

rkus2zg0

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2022-08-25

Find d y d x by implicit differentiation
x 2 4 x y + y 2 = 4
I know to take the derivatives of both sides, which would be:
d d x [ x 2 4 x y + y 2 ] = 0
I'm not sure if I did it right, but I then got:
2 x 4 ( x d y d x ) + y + 2 y ( d y d x ) = 0
I don't know where to go from here, or even if the previous step is correct. Please help!
Edit: I have followed the advice given and I ended up with:
x 2 y 2 x 1
However this was incorrect. Someone please tell me what I am missing here.

Answer & Explanation

Paityn Arroyo

Paityn Arroyo

Beginner2022-08-26Added 5 answers

You are close! You forgot a coefficient on the y term. You should have
2 x 4 y 4 x d y d x + 2 y d y d x = 0
Now you can solve for d y d x like any other variable.

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