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Calculus 1 - implicit differentiation

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I do not understand implicit differentiation. One of the problems are: find y' by implicit differentiation xy+2x+3x^2=4.

I would appreciate any help that can be offered.

  • Calculus 1 - implicit differentiation -

    Just differtiate each term with respect to x, remembering that y is a function of x. You often end up with an expression for y' that involves both x and y, but is is a valid equation. You may have to evaluate y before you can calculate y'. Here is what you get:

    x*dy/dx + y + 2 + 6x = 0
    dy/dx = -(y + 2 + 6x)/x
    = -(y+2)/x -6

  • Calculus 1 - implicit differentiation -

    thank you

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