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

cos(2*pi*x)*(2*pi*x)'

cos(2*pi*x)*((2*pi)'*x+2*pi*(x)')

cos(2*pi*x)*(0*x+2*pi*(x)')

cos(2*pi*x)*(0*x+2*pi*1)

2*pi*cos(2*pi*x)

2*pi*cos(2*pi*x)

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