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Find dy/dx by implicit differentiation.

y^5 + x^2y^3 = 1 + x^4y

So, first I find the derivative:

5y^4 + 2x3y^2 = 4x^3(1)

Now I find dy/dx:

But this is where I don't know what to do?

Please Help.

  • Calc -

    Did I do the derivative part wrong?

    Should it be:

    5y^4 + (x^2 . 3y^2 + y^3 . 2x) = (x^4 . 1 + y . 4x^3)

  • Calc -

    you appear to be very very confused.
    y^5 + (x^2)(y^3) = 1 + (x^4)(y)

    remember you are finding dy/dx, so you are differentiating with respect to x
    Which means that when you differentiate a y term you will have dy/dx tagging along

    5y^4 dy/dx + (x^2)(3y^2)dy/dx + (y^3)(2x) = 0 + x^4 dy/dx + y(4x^3)

    get all dy/dx terms to the left side

    5y^4 dy/dx + 3x^2(y^2) dy/dx - x^4 dy/dx = 4y(x^3) - 2x(y^3)

    dy/dx = (4y(x^3) - 2x(y^3)) / (5y^4 + 3x^2(y^2) - x^4 )

    check my typing, easy to make an error with all those exponents

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