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(ln(tan(4*x)))'The calculation above is a derivative of the function f (x)

(1/tan(4*x))*(tan(4*x))'

(1/tan(4*x))*((4*x)'/((cos(4*x))^2))

(1/tan(4*x))*(((4)'*x+4*(x)')/((cos(4*x))^2))

(1/tan(4*x))*((0*x+4*(x)')/((cos(4*x))^2))

(1/tan(4*x))*((0*x+4*1)/((cos(4*x))^2))

(4/((cos(4*x))^2))/tan(4*x)

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