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

(1/sin(2*x))*(sin(2*x))'

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

(1/sin(2*x))*cos(2*x)*((2)'*x+2*(x)')

(1/sin(2*x))*cos(2*x)*(0*x+2*(x)')

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

2*(1/sin(2*x))*cos(2*x)

(2*cos(2*x))/sin(2*x)

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