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Find the Derivative

  1. Mar 20, 2013 #1
    1. The problem statement, all variables and given/known data


    Find dy/dx: 4a^2b - 3b^2 = a^3 Please SIMPLIFY this one







    Find f'(x): f(x) = (3x^4) [6/(3√x^5)] (6x^2 - 3x)^5 The middle is 6 divided by the cube root of x^5, Please do not simplify fully for this one and use the product rule








    3. The attempt at a solution

    i got - (8ab - 3a^2)/(4a^2 - 6b) using the implicit rule
    However I need some help simplifying


    For the second one, would my approach be (derivative of first)(original second)(original third) + (derivative of second)(original first)(original third) + (derivative of third)(original first)(original second) ?
     
    Last edited: Mar 20, 2013
  2. jcsd
  3. Mar 20, 2013 #2
    Think makes no sense to me.

    What are you trying to do?
     
  4. Mar 20, 2013 #3

    haruspex

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    Your approach for the second is fine. The first is unintelligible. Please check what you wrote.
     
  5. Mar 20, 2013 #4
    Is this not the result of the implicit method? Should I not even be using the implicit method? I thought I had to with numerator being the derivative with respect to "a" and the denominator the derivative with respect to "b"
     
  6. Mar 20, 2013 #5
    How should we know what you need to do if its not even clear what you're question asking?

    You just simply said Find dy/dx, then gave an expression in terms of a and b then said simplify.

    What does that even mean?
     
  7. Mar 20, 2013 #6
    Sorry about the a and b, it should be a=x and b = y (teacher gave it to us like that) but the question is to simply find the derivative (dy/dx).... i dont know what more I can tell you...
     
  8. Mar 20, 2013 #7

    haruspex

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    Ok, but it still doesn't make sense: Find dy/dx: 4x2y - 3y2 = x3. What's the equals sign doing?
     
  9. Mar 20, 2013 #8
    I have to set it equal to zero and use implicit differentiation
     
  10. Mar 20, 2013 #9

    haruspex

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    Sorry, I was confusing two questions. Your answer looks right.
     
  11. Mar 20, 2013 #10
    Ok Thank you! but is that all it can be simplified down to?
     
  12. Mar 20, 2013 #11

    haruspex

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    You could factorise out an x in the numerator, but other than that, that's as simple as it will go.
     
  13. Mar 20, 2013 #12
    May I ask you one more question? How would i find the derivative of (1/x) + (1//y) = 1 using implicit and for a question like (x^2/19) - (y^2/9) = 1 would I find the common denominator and then go through with implicit differentiation?
     
  14. Mar 21, 2013 #13

    haruspex

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    You can just differentiate straight away. What's the difficulty? Yes, multiplying out first might make it a little simpler.
     
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