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