AP Calculus question

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The correct answer is e, but I don’t see how they got that. I did implicit differentiation and got 1-15x^2/-4-4y

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7 Responses to AP Calculus question

  1. mindweapon says:

    Oops, I think I got it. I had to do product rule on 4xy. However, I ended up with 4y -15x^2/-4x-4y

    The answer looks like it pulled the negative sign out of 4y-15x^2. But apparently you can do this without affecting the signs of the denominator, the -4x-4y? Signs in fractions confuse me.

  2. OSEverything says:

    Think of the negative sign as being (-1). Now you can look at it like this:

    (-15x^2+4y)/(-4x-4y) = (-1)(15x^2-4y)/(-4x-4y) = (-15x^2+4y)/[(-1)(4x+4y)] = (-1)(15x^2-4y)/[(-1)(4x+4y) = (15x^2-4y)/(4x+4y)

    All of those solutions are equally correct, but part of learning math is being able to “see” all these equivalencies.

  3. Mr. Rational says:

    Let me see if I can still do this.

    5x³ – 4xy – 2 y² = 1

    d( 5x³ – 4xy – 2 y² ) = d(1) = 0

    15x²dx – 4ydx – 4xdy – 4ydy = 0

    (15x²-4y) dx – 4(x-y) dy = 0

    (15x²-4y) dx = 4(x-y) dy

    dy/dx = (15x²-4y) / 4(x-y) which is the same as (e).

    • Mr. Rational says:

      This idiot blog software doesn’t even pass the escape for 2-superscript?!  What moron wrote this piece of junk?

  4. Answer e is correct but the negative sign before the fraction and the negative signs in the denominator should be removed.

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