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Math Help - Implicit Differentiation of a Function

  1. #1
    Junior Member StarlitxSunshine's Avatar
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    Implicit Differentiation of a Function

    Find the indicated derivative through implicit differentiation:

    a^4-t^4 = 6a^2t; da/dt = ?

    4a^3da/dt - 4t^3 = 12a*da/dt

    I took the terms with da/dt to one side, took common and then divided to the other side to get:

    \frac{-t^3}{3a-a^3}

    Which is not the real answer:
    \frac{2t^3+3a^2}{2a^3-6at}
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  2. #2
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    Quote Originally Posted by StarlitxSunshine View Post
    Find the indicated derivative through implicit differentiation:

    a^4-t^4 = 6a^2t; da/dt = ?

    4a^3da/dt - 4t^3 = 12a*da/dt

    This is not implicit, or any other, differentiation! You must do:

    4a^3da-4t^3dt=12atda+6a^2dt , and then gather togeter simmilar terms and stuff.

    Tonio

    I took the terms with da/dt to one side, took common and then divided to the other side to get:

    \frac{-t^3}{3a-a^3}

    Which is not the real answer:
    \frac{2t^3+3a^2}{2a^3-6at}
    .
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  3. #3
    Junior Member StarlitxSunshine's Avatar
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    How can you separate da & dt ?
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    Quote Originally Posted by StarlitxSunshine View Post
    How can you separate da & dt ?

    Gather simmilar terms together and use parentheses!

    Tonio
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