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(ln(ln(2-cos(x))))'The calculation above is a derivative of the function f (x)

(1/ln(2-cos(x)))*(ln(2-cos(x)))'

(1/ln(2-cos(x)))*(1/(2-cos(x)))*(2-cos(x))'

(1/ln(2-cos(x)))*(1/(2-cos(x)))*((-cos(x))'+(2)')

(1/ln(2-cos(x)))*(1/(2-cos(x)))*((2)'-sin(x))

(1/ln(2-cos(x)))*(1/(2-cos(x)))*(sin(x)+0)

(sin(x)/(2-cos(x)))/ln(2-cos(x))

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