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Math Help - find the equation of a tangent line (calc)

  1. #1
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    find the equation of a tangent line (calc)

    Hey guys!
    Here's a question on a math test (with solutions) that I don't understand very well:



    So for the first step, i understand what they did, and how they got the point on the graph.

    For the second step, i see they pulled out 4x and i understand how they get 3y^2y' but i dont understand how they got 4y^3 and 15y^2y'

    could anyone help me with that?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    4xy^3 + 27 = 5y^3

    Using implicit differentiation, 4xy^3 becomes:

    4x\cdot 3y^2 y' + y^3\cdot 4 = 12xy^2y' + 4y^3

    Differentiating 5y^3:

    5(3y^2)y' = 15y^2y'

    Is this okay?
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  3. #3
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    yes! thanks, i get it!
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