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Math Help - Implicit differentiation

  1. #1
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    Implicit differentiation

    For some questions on finding dy/dx implicitly, e.g. \sqrt{1+x^{2}y^{2}}=2xy, it is easier if we square both sides first.

    My question is this, when I square both sides of the equation, will I ALWAYS get the correct dy/dx? Will I "change" the question if I square both sides?

    Thanks!
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  2. #2
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    Quote Originally Posted by acc100jt View Post
    For some questions on finding dy/dx implicitly, e.g. \sqrt{1+x^{2}y^{2}}=2xy, it is easier if we square both sides first.

    My question is this, when I square both sides of the equation, will I ALWAYS get the correct dy/dx? Will I "change" the question if I square both sides?

    Thanks!
    As is often the case when you square both sides of an equation to make caculations easier, you may get extraneous answers.
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    To clarify on what Prove It said, you may arrive at extraneous solutions in addition to the valid solution(s), but the valid solution(s) (if any exist) will not be lost.
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