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Differentiation - chain and product rule.

  1. Sep 2, 2011 #1
    It's been years since I've done maths properly so I'm rusty with it. I'm helping out a colleague at work who is studying maths for an OU course.

    1. The problem statement, all variables and given/known data

    Part 1: Differentiate function.
    f(x) = e^(0.5x+cos(x))

    Part 2: Use answer from part 1 to show.
    g(x) = (1+2sinx)(e^(0.5x+cos(x)))
    Has the derivative:
    g'(x) = 0.5(4cos^2(x)+4cos(x)-3)(e^(0.5x+cos(x)))


    3. The attempt at a solution

    A=e^(0.5x+cos(x))

    Part 1:
    Using chain rule
    f'(x) = A(0.5-sin(x))


    Part 2:
    Using this and the product rule I get.

    g'(x) = 0.5A(4cos(x)-4sin^2(x)+1)


    Which isn't the same.
     
  2. jcsd
  3. Sep 2, 2011 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, it is the same. Use the fact that [itex]sin^2(x)= 1- cos^2(x)[/itex].
     
  4. Sep 2, 2011 #3
    Ahh I forgot about that, thanks.
     
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