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(x*sin(1/x))'The calculation above is a derivative of the function f (x)

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

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

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

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

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

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

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

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

sin(1/x)+x^-1*cos(1/x)

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