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

(e^cos(x))'*ln(2*x)+e^cos(x)*(ln(2*x))'

e^cos(x)*((cos(x))'*ln(e)+(cos(x)*(e)')/e)*ln(2*x)+e^cos(x)*(ln(2*x))'

e^cos(x)*((cos(x))'*ln(e)+(cos(x)*0)/e)*ln(2*x)+e^cos(x)*(ln(2*x))'

e^cos(x)*((cos(x)*0)/e-sin(x)*ln(e))*ln(2*x)+e^cos(x)*(ln(2*x))'

e^-sin(x)*ln(2*x)+e^cos(x)*(ln(2*x))'

0^cos(x)*ln(2*x)+e^cos(x)*(ln(2*x))'

e^cos(x)*(ln(2*x))'-(e^cos(x)*sin(x))*ln(2*x)

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

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

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

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

e^cos(x)*x^-1-(e^cos(x)*sin(x))*ln(2*x)

x^-1*e^cos(x)-(e^cos(x)*sin(x)*ln(2*x))

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