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Math Help - differentiate

  1. #1
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    differentiate

    how do you differentiate ln|cscx + cotx|
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  2. #2
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    Hello, algebra2!

    How do you differentiate: . f(x) \:=\:\ln|\csc x + \cot x|

    Chain Rule: . f'(x) \;=\;\frac{1}{\csc x + \cot x}\cdot(\text{-}\csc x\cot x - \csc^2\!x)

    Factor: . f'(x) \;=\;\frac{\text{-}\csc x\left(\cot x + \csc x\right)}{\csc x + \cot x}

    Reduce: . f'(x) \;=\;\text{-}\csc x

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  3. #3
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    Quote Originally Posted by algebra2 View Post
    how do you differentiate ln|cscx + cotx|
    Also note that \int \ \frac{f'(x)}{f(x)}= \ln|f(x)| + c. For example \int \ \frac{1}{x}= \ln|x| + c thus \frac{\mathrm{d}\left(\ln |x|\right)}{\mathrm{d}x} = \frac{1}{x}

    Hence: \frac{\mathrm{d}\left(\ln|\csc x + \cot x |\right)}{\mathrm{d}x} = \frac{\left(\csc x + \cot x \right)'}{\csc x + \cot x} = ...
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