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Implicit Differentiation

  1. Dec 12, 2005 #1
    Assume that y is a function of x . Find y' = dy/dx for (x^3+y^3)^20

    when i solved this i got y'= (20(x^3+y^3)^19 * 3x^2)/(-3y^2)

    is this correct or am i missing something?
  2. jcsd
  3. Dec 12, 2005 #2


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    It's not entirely right, remember that y(x) is an unknown function of x!

    y = \left( {x^3 + y^3 } \right)^{20} \hfill \\
    y' = 20\left( {x^3 + y^3 } \right)^{19} \cdot \left( {x^3 + y^3 } \right)^\prime = 20\left( {x^3 + y^3 } \right)^{19} \cdot \left( {3x^2 + 3y^2 \cdot y'} \right) \hfill \\

    Now you can solve for y'.
  4. Dec 12, 2005 #3
    thanks a lot man. the grader only took off 3 pts for that prob and didnt say anything else, so i didnt know what i did wrong.

    THANKS A LOT, you just saved me from making several mistakes on my final exam tommorow :D
  5. Dec 13, 2005 #4


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    Good luck! :smile:
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