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Math Help - Derivative of a trig function

  1. #1
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    Derivative of a trig function

    Is f'(x) = -2sinx + 2cos2x the derivative of f(x) = 2cosx + sin2x ? I have no way to check if I am correct.
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    Quote Originally Posted by jmhogart View Post
    Is f'(x) = -2sinx + 2cos2x the derivative of f(x) = 2cosx + sin2x ? I have no way to check if I am correct.
    Looks right to me
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    Ok thank you... now how might I go about setting the derivative equal to 0 and solving in order to find critical numbers?
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    Quote Originally Posted by jmhogart View Post
    Is f'(x) = -2sinx + 2cos2x the derivative of f(x) = 2cosx + sin2x ? I have no way to check if I am correct.
    Quote Originally Posted by jmhogart View Post
    Ok thank you... now how might I go about setting the derivative equal to 0 and solving in order to find critical numbers?
    f'(x)= 2cos(2x) - 2sin(x) = 0

    2cos(2x) = 2sin(x)

    We know that 2 will cancel and cos(2x) = 1-2sin^2(x). Substitute and move sin(x) back to the other side.

    1-2sin^2(x)-sin(x)=0 \rightarrow 2sin^2(x)+sin(x) - 1 = 0

    Let u = sin(x) and solve the quadratic for u then do arcsin(u).
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