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Math Help - implicit differentiation

  1. #1
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    implicit differentiation

    I have a quick question regarding implicit differentiation:
    Heres the problem and its solution
    .



    What I dont understand is from the 1st step (First arrow) to the second, in particular why the x^2 turns into y^2 in 2xycos(y^2). The same goes on the right side. Why isnt it y'[2xycos(x^2)+sin(x^2)]=-sin(y^2)-2xycos(y^2)?

    Also, on the right side there is a y' which seems to disappear?

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Evan.Kimia View Post
    I have a quick question regarding implicit differentiation:
    Heres the problem and its solution
    .



    What I dont understand is from the 1st step (First arrow) to the second, in particular why the x^2 turns into y^2 in 2xycos(y^2). The same goes on the right side. Why isnt it y'[2xycos(x^2)+sin(x^2)]=-sin(y^2)-2xycos(y^2)?

    Also, on the right side there is a y' which seems to disappear?

    Thanks in advance.
    They collected all the terms which had a y' on one side of the equation and all the terms without on the other side.

    This is so you can take out a common factor of y' and thus solve for y'.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    They collected all the terms which had a y' on one side of the equation and all the terms without on the other side.

    This is so you can take out a common factor of y' and thus solve for y'.
    Ohhh. I remember now, thank you for clarifying.
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