Question:

Using implicit differentiation find dy/dx ?

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if:

y^3 - 3xy + e^y = x^2

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  1. 3y² dy/dx - 3y - (3x) dy/dx + e^y dy/dx = 2x

    ( 3y² - 3x + e^y ) ( dy/dx ) = 2x + 3y

    dy/dx = (2x + 3y) / (3y² - 3x + e^y)


  2. differentiate...

    3y^2dy/dx - (3xdy/dx + 3y) + e^ydy/dx  = 2x

    get dy/dx's on one side...

    3y^2dy/dx - 3xdy/dx + e^ydy/dx = 2x + 3y

    factor out dy/dx and divide out...

    dy/dx = (2x + 3y)/(3y^2 - 3x + e^y)
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