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Find the derivative of the function

  1. Jan 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Screenshot2012-01-25at63328PM.png

    3. The attempt at a solution


    I don't understand how in the final step they got the numerator. Where's the 45 come from? what happened to 2t+1?, or in the denominator they got (2t+1) raised to the 10th power.
     
    Last edited: Jan 25, 2012
  2. jcsd
  3. Jan 25, 2012 #2

    Dick

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    h'(x)=2. Why do you say '2 or 1'?? And (2t+1)*1-2*(t-2)=5. Multiply it out. Finally [itex]({\frac{t-2}{2t+1})}^8=\frac{(t-2)^8}{(2t+1)^8}[/itex]. Does that help?
     
    Last edited: Jan 25, 2012
  4. Jan 25, 2012 #3
    You read my post before I edited it. I'm still having trouble getting 45, and the 10th power in the denominator.
     
  5. Jan 25, 2012 #4

    Dick

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    9*5=45. And (2t+1)^8*(2t+1)^2=(2t+1)^10.
     
  6. Jan 25, 2012 #5
    Ok, I figured out the numerator, I can get 45 now. But I still can't get the 10th power in the denominator.
     
  7. Jan 25, 2012 #6
    9 ((t - 2)/(2t + 1))^8 ((2t + 1)(1) - (2)(t -2))/(2t + 1)^2)

    9 ((t - 2)/(2t + 1))^8 (2t + 1 - 2t + 4)/(2t + 1)^2

    Simplify from here.

    Also, ((t - 2)/(2t + 1))^8 is the same as (t - 2)^8/(2t + 1)^8
     
  8. Jan 25, 2012 #7
    Thanks, I got it now.
     
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