Find (dy)/(dx) by implicit differentiation. x^2−4xy+y^2=4

batejavizb 2022-09-14 Answered
Find dydx by implicit differentiation.
x2−4xy+y2=4

My solution:
d d x x 2 d d x 4 x y + d d x y 2 = d d x 4
2 x ( 4 x ) ( y ) + ( 4 x ) ( y ) + 2 y d y d x = 0
2 x 4 y d y d x + 4 x d y d x + 2 y d y d x = 0
d y d x ( 4 y + 4 x + 2 y ) = 2 x
d y d x = 2 x 4 x 2 y
Correct answer:
d y d x = 2 y x y 2 x
I would like to understand why my answer is incorrect. If someone could take a look at my steps and explain to me where I went wrong it would be greatly appreciated!
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Answers (1)

Kelbelol
Answered 2022-09-15 Author has 9 answers
The third line should be
2 x 4 y 4 x d y d x + 2 y d y d x = 0
not
2 x 4 y d y d x + 4 x d y d x + 2 y d y d x = 0
and that plus sign error was also in the second line.

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