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Differentiating a function

  1. Apr 11, 2009 #1

    TG3

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    The problem statement, all variables and given/known data

    Differentiate sin x - 1/3 sin^3 (x) + 7

    The attempt at a solution

    sin x becomes cos x, and 7 becomes 0.
    Using the product rule on (1/3) sin^3 (x) + 7 I get:
    (0) sin^3 x + (1/3) [derivative of sin^3 (x)]

    Getting the derivative of sin^3(x) is the tricky part I'm struggling with.
    I would have thought it would be 3 sin^2 (x) times cos^3(x); but I know this is wrong.
     
  2. jcsd
  3. Apr 11, 2009 #2
    think of (1/3)*sin^3(x) as (1/3)*(sin x)^3 then apply the chain rule :)
     
  4. Apr 11, 2009 #3
    f(x) = sin x - 1/3 sin^3 (x) + 7

    f '(x) = cos(x) - 1/3 * 3(sin(x))^2 * cos(x) + 0
    = cos(x) - sin(x)^2 * cos(x)
     
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