Find, ^2y^2−2xy+x=2 find the slope and the equation of the tangent line at (2,0) by implicit differentiation.

Taniya Burns

Taniya Burns

Answered question

2022-07-22

Find,
x 2 y 2 2 x y + x = 2
find the slope and the equation of the tangent line at (2,0) by implicit differentiation.
Part of the problem is that my text book says find d / d x and then ignore d y / d x after I get
x 2 y 2 = 2 x 2 y
Please show me where I am going wrong. I would be able to find the equation of the tangent line if I had the correct f ( x )

Answer & Explanation

Sandra Randall

Sandra Randall

Beginner2022-07-23Added 17 answers

Not sure what you are doing, but this is my take. Hope it helps.
d d x ( x 2 y 2 ) d d x ( 2 x y ) + d d x ( x ) = 0
Then, remember that d d x ( y 2 ) = d d y ( y 2 ) d y d x = 2 y y (chain rule). Then, using product rule and chain rule, we have
( 2 x y 2 + x 2 2 y y ) ( 2 y + 2 x y ) + 1 = 0 y = y x y 2 + 1 / 2 x 2 y x
Look over the Chain rule again, especially when you have y in the expression you are differentiating.
Leila Jennings

Leila Jennings

Beginner2022-07-24Added 5 answers

For your information, to ignore d y / d x is a horrible advice. Use a reliable textbook. You should be solving for d y / d x instead.

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