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Homework Help: Value of the differential of tan(x)^cos(x) at pi/4

  1. Jun 21, 2012 #1
    1. The problem statement, all variables and given/known data
    ^


    2. Relevant equations



    3. The attempt at a solution

    y = tanx^cosx

    lny = cosx(ln(tanx))

    1/y(dy/dx) = (sec^2x * cosx)/tanx + ln(tanx)(-sinx)

    at pi/4

    1/y(dy/dx) = (1 * 1/sqrt(2))/1 + ln(1)(-sin(pi/4))

    1/y(dy/dx) = 1/sqrt(2) + 0 ******* ln1 = 0

    ***
    y = tanx^cosx => 1^(1/sqrt(2)) = 1 => 1/y = 1
    ***
    dy/dx at pi/4 = 1/sqrt(2)

    The answer is sqrt(2) NOT 1/sqrt(2)

    What am I doing wrong?
     
  2. jcsd
  3. Jun 21, 2012 #2

    SammyS

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    Hello ishant. Welcome to PF !

    What is sec2(π/4) ?
     
  4. Jun 21, 2012 #3
    Oh my god! Thank you!
     
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