Find, x 2 y 2 − 2 x y + x = 2find 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 yPlease 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 )

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Find,      x    2        y    2    −  2  x  y  +  x  =  2find 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    yPlease 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  )

Sandra Randall · Accepted Answer

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    )    =  0Then, 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 · Accepted Answer

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.

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

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