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F(e^(2x)), derivative = ?

  1. Nov 3, 2005 #1
    I just did the first part of two final high school year exams. And I came across this question that stumped me. It said:
    * means multiplication
    Let f:R --> R be a differentiable function. For all real values of x, the derivative of f(e^(2x)) with respect to x will be equal to:

    A. 2e^(2x) * f '(x)
    B. e^(2x) * f '(x)
    C. 2e^(2x) * f '(e^(2x))
    D. 2 * f '(e^(2x))
    E. f '(e^(2x))

    Having never come across these types of questions before, I selected E. Some of my friends selected C but none of us are really sure because it hasn't been in any of the past papers from 1994-2004. If it's not E, why can't it be E?

  2. jcsd
  3. Nov 3, 2005 #2
    What happens there is:{F(e^(2x))'= F'(x)d(e^(2x)=F'(x)*2e^(2x)

    It can't be E because of the chain rule D(F(g(x))=F'(g(x)*g'(x).
  4. Nov 3, 2005 #3
    /cry One mark lost
  5. Nov 4, 2005 #4
    I did that exam too, and don't worry about losing 1 mark, i've lost 4 already!! :(

    it would seem I got this question wrong as well, I just couldn't think. I hadn't seen anything like that before either in practice exams, and so just assumed it was a simple trick question and put E.

    I got #22 and #27 wrong in multiple choice, most likely #15 as well because I just know nothing about dilation etc., and forgot to state the domain of the inverse in the short answer. Does "specify the rule" or whatever the instruction was imply that you need the domain?

    I just put down B for #27 without even looking at choice A, i'm so stupid.

    I just hope i haven't lost any more than 4, because after that it isn't an A+ I think.

    Just to clear up #15 with the help of some people here, it's probably obvious to others but not to me.

    -The graph of the function with rule y=x^3 is transformed as follows:
    a translation of-2 units parallel to the x-axis
    and then
    a dilation by a factor of 1/2 from the y-axis

    The rule of the function corresponding to the transformed graph is

    A. y= (1/2)(x-2)^3
    B. y=2(x-2)^3
    C. y=((x/2)+2)^3
    D. y=2(x+2)^3
    E y= (2x+2)^3

    I selected D, but as i stated, i haven't read that chapter of the textbook :p
    Last edited: Nov 4, 2005
  6. Nov 4, 2005 #5
    its E, y=(2x+2)^3, 27 was also hard, luckily i found out how to do it. Did you also simplify your derivative from ln(3) * e^(x*ln(3)) to 3^(x) * ln(3), its the last question of the short answers. I didn't and hopefully they don't deduct marks for not simplifying.
  7. Nov 4, 2005 #6
    I left it like that as well, I really don't think they'd take a mark off for not simplifying it, atleast they better not!!
  8. Nov 4, 2005 #7


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    laaah, it would have been "D" if they did the translation after the dialation, but since the dialation is done last then the answer is "E" as erzeon said.
  9. Nov 4, 2005 #8
    In regards to the first post i was under the impression that it answer was C. That is dy/dx=du/dx*dy/du, where u is e^(2x) . As in the case of the derivative of cos( e^(x) ), which is - 2e^(2x)*sin (e^(2x)).
    Last edited: Nov 5, 2005
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