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Math Help - differentiation

  1. #1
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    differentiation

    This is the problem

    If g(x) = (ax^2 + bx + c) sinx + (dx^2 + ex + f) cos x

    determine the values of the constants a, b, c,d,e, f

    such that g'(x) = x^2 sinx
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  2. #2
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    Quote Originally Posted by ClipsClips99 View Post
    This is the problem

    If g(x) = (ax^2 + bx + c) sinx + (dx^2 + ex + f) cos x

    determine the values of the constants a, b, c,d,e, f

    such that g'(x) = x^2 sinx
    g \prime (x) = (2ax + b)sin(x) + (ax^2 + bx + c)cos(x) + (2dx + e)cos(x) - (dx^2 + ex + f)sin(x)

    = (-dx^2 + [2a - e]x + [b - f])sin(x) + (ax^2 + [b + 2d]x + [c + e])cos(x)

    = x^2 sin(x)

    So by matching up the coefficients I get
    -d = 1
    2a - e = 0
    b - f = 0
    a = 0
    b + 2d = 0
    c + e = 0

    This gives me the solution:
    a = 0
    b = 2
    c = 0
    d = -1
    e = 0
    f = 2

    -Dan
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