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Derivative of e

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the derivative of the given function
    z=(te^6t + e^7t)^5


    2. Relevant equations



    3. The attempt at a solution
    5(te^6t + e^7t)^4
     
  2. jcsd
  3. Oct 25, 2009 #2

    Dick

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    That's wrong! Chain rule! Then product rule!
     
  4. Oct 25, 2009 #3

    lurflurf

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    write
    z=(te^6t + e^7t)^5=(t+e^t)^5*e^30t
     
    Last edited: Oct 25, 2009
  5. Oct 25, 2009 #4

    Dick

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    You mean z=(t+e^t)^5*e^30t. And I don't see how that makes it easier. The original form for z is easy enough to differentiate if you use the rules.
     
  6. Oct 25, 2009 #5

    lurflurf

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    They are both easy, but I thought the use of slightly fewer rules was an improvement.
    (te^6t + e^7t)^5
    power rule with chain rule
    sum rule
    product rule
    derivative of an exponential with chain rule x2
    derivative of the variable
    total=9 rules (3 chain)
    vs
    (t+e^t)^5*e^30t
    product rule
    derivative of an exponential with chain rule
    power rule with chain rule
    sum rule
    derivative of the variable
    derivative of an exponential
    total=8 rules (2 chain)
    Though most important
    (t+e^t)^5*e^30t is more aesthetically pleasing to my eye.
     
  7. Oct 25, 2009 #6

    Dick

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    Well, now it's up to neutron star to pull off either one.
     
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