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

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

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

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

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

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

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