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Homework Help: Differentiation using product rule?

  1. Apr 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Differentiate the following function with respect to x,
    p(x) = (( x+5 )^2)*(( x+3 )^7)


    2. Relevant equations
    well the product rule is,
    p(x)=(f)*(g)
    p'(x)= (f')*(g)+(g')*(f)
    and general differentiation is,
    p'(x)=n(f)^(n-1)*n(g)^(n-1)

    3. The attempt at a solution
    well i used the product rule and got
    (2(x+5))*((x+3)^7)+(7(x+3)^6)*((x+5)^2)
    but this is said to be wrong how do i simplify it more or what have i done wrong???
     
  2. jcsd
  3. Apr 18, 2010 #2

    Dick

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    What you did is right. They probably just want you to pull out the common factors to simplify it more.
     
  4. Apr 18, 2010 #3
    so i could go,
    (2*x+10)*(x+3)^7+(7x+21)*(x+5)^2
    then
    (3x+13)^7+(8x+26)^2
     
  5. Apr 18, 2010 #4

    Dick

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    Your algebra is looking pretty seriously awful there. Whoa. Just factor out (x+5)*(x+3)^6 and collect the rest. Try and use only real algebra this time, and not just random symbol rearrangment, ok?
     
  6. Apr 19, 2010 #5
    so it works out to be,
    ((x+3)^6)*((9x^2)+(86x)+205)
    cheers for the help
     
  7. Apr 19, 2010 #6

    Dick

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    That's one version. You could also write it as (x+3)^6*(x+5)*(9x+1). Whatever works, like I said your initial differentiation was correct as well.
     
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