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Easy Derivative - Not easy for me, though!

  1. Nov 18, 2007 #1
    1. Derivate x^(2sinx)


    3. I used implicit differentiation because there's an x in the base and in the exponent.
    I have all of my work in the picture (if you cant see it in the attachment):

    http://i12.tinypic.com/7x1sn44.jpg


    I don't get the same answer as the correct answer which is 2cosx(x^2sinx), and I can't figure out why!!

    Am I doing something wrong, or is it possible the answer is wrong !?
     

    Attached Files:

  2. jcsd
  3. Nov 18, 2007 #2
    Try substituting t = 2 sin x and you will get x^t where t(x). Differentiate x^t. What are you going to do if you get any t':s in your equation?
     
  4. Nov 18, 2007 #3
    i'm getting the same answer as you
     
  5. Nov 18, 2007 #4
    ya i just i checked my answer using a graph - its right and the other answer is wrong - thanks!
     
  6. Nov 18, 2007 #5
    anytime :-]
     
  7. Nov 18, 2007 #6

    dynamicsolo

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    Homework Helper

    Whoever provided the 'correct' answer just treated it like d/dx (a^u), which only works for a constant a > 0. When the base of the exponential function is itself a variable or function, logarithmic differentiation is called for, which is what you did. (I sure hope that wasn't a TA or instructor who wrote that 'answer'...)
     
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