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Differentiating a trig function to the power of 2

  1. Aug 12, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm doing a optimisation question and I get to a point where I have to verify a maximum using a double derivative and I need to differentiate -5sin^2(x)

    2. Relevant equations
    -5sin^2(x)


    3. The attempt at a solution
    -10cos(x)sin(x) im not sure if the answer is positive or negative.
     
  2. jcsd
  3. Aug 12, 2011 #2
    -10cos(x)sin(x) would be your first derivative .
     
  4. Aug 12, 2011 #3

    HallsofIvy

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    You are using the chain rule: [itex]-5sin^2(x)[/itex] can be written as [itex]-5u^2[/itex] with [itex]u= sin(x)[/itex]. The derivative of [itex]-5u^2[/itex], with respect to u, is -10u and the derivative of [itex]u= sin(x)[/itex] with respect to x is [itex]cos(x)[/itex]. Multiply those together.
     
  5. Aug 12, 2011 #4
    it is negative and in order to find maximum value you have to differentiate once more
     
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