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Math Help - compound trig function

  1. #1
    Senior Member furor celtica's Avatar
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    compound trig function

    differentiate wrtx the function ln(cosx)
    i found -(sinxcosx)/x but the right answer is -tanx
    why is this?
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  2. #2
    Super Member
    earboth's Avatar
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    Quote Originally Posted by furor celtica View Post
    differentiate wrtx the function ln(cosx)
    i found -(sinxcosx)/x but the right answer is -tanx
    why is this?
    f(x)=\ln(\cos(x))~\implies~f'(x)=\underbrace{\dfra  c{1}{\cos(x)}}_{\text{der. of ln}} \cdot \underbrace{(-\sin(x))}_{\text{der. of cos}} = -\dfrac{\sin(x)}{\cos(x)} = -\tan(x)
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