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Homework Help: Find The Derivative

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data

    y =x4(2x-5)6

    2. Relevant equations

    Product Rule & Power of a Function Rule

    3. The attempt at a solution

    y = x4(2x-5)6
    y' = 4(x)3(1)(2x-5)6 + x4(6)(2x-5)5(2)
    y' = 4x3(2x-5)6 + 12x4(2x-5)5

    The answer is:
    20x3(2x-5)5(x-1)

    No idea where they get the 20x3 or the (x-1). If I were to factor my answer, I still wouldn't get that, I think.
     
  2. jcsd
  3. Feb 25, 2010 #2

    Mark44

    Staff: Mentor

    Your answer is correct but unfactored. Pull the greatest common factor (GCF) out of the two separate terms, as shown below.
    4x3(2x - 5)6 + 12x4(2x - 5)5
    = 4x3(2x - 5)5(2x - 5 + 3x)
    = 4x3(2x - 5)5(5x - 5)
    = 5*4x3(2x - 5)5(x - 1)
    = 20x3(2x - 5)5(x - 1)
     
  4. Feb 25, 2010 #3
    Thanks!

    Can you help me out with one more?

    y = (1-x2)3 (6+2x)-3
    y' = 3 (1-x2)2 (-2x)(6+2x)-3 + (1-x2)3(-3)(6+2x)-4(2)
    y' = -6x (1-x2)2(6+2x)-3 - 6(1-x2)3(6+2x)-4

    Not exactly sure what to do with this.

    I could possibly:
    y' = -6 (1-x2)(6+2x)-3[x-(1-x2)(6+2x)-1]

    or should I put the (6+2x) on the bottom:
    y' = -6x(1-x2)2 - 6(1-x2)3
    ......---------- .. ----------
    ........(6+2x)3 ..... (6+2x)4


    The answer is:

    -6(1-x2)2(x2+6x+1)
    -------------------
    ........(6+2x)4
     
  5. Feb 25, 2010 #4

    Mark44

    Staff: Mentor

    The common factor is 6(1 - x2)2(6 + 2x)-4. Pull that out and then combine what's left.
     
  6. Feb 25, 2010 #5
    y = (1-x2)3 (6+2x)-3
    y' = 3 (1-x2)2 (-2x)(6+2x)-3 + (1-x2)3(-3)(6+2x)-4(2)
    y' = -6x (1-x2)2(6+2x)-3 - 6(1-x2)3(6+2x)-4

    That's kind of the problem. I'm not sure how to take out < -6(1 - x2)2(6 + 2x)-4 >.

    In the 3rd line, there is a (6+2x)-3, how do you take out (6+2x)-4? Does the power become a positive, and therefore: (6+2x)1 which is just (6+2x)?
     
  7. Feb 25, 2010 #6
    Nevermind. I got it.

    Thanks for the help!
     
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