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

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

(1/sin(4*x))*cos(4*x)*(4*x)'

(1/sin(4*x))*cos(4*x)*((4)'*x+4*(x)')

(1/sin(4*x))*cos(4*x)*(0*x+4*(x)')

(1/sin(4*x))*cos(4*x)*(0*x+4*1)

4*(1/sin(4*x))*cos(4*x)

(4*cos(4*x))/sin(4*x)

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