Derivative of ln(ctg(3x))

Derivative of ln(ctg(3x)). Simple step by step solution, to learn. Simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

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Derivative of ln(ctg(3x)): 


(ln(ctg(3*x)))'

(1/ctg(3*x))*(ctg(3*x))'

(1/ctg(3*x))*(-(3*x)'/((sin(3*x))^2))

(1/ctg(3*x))*((-((3)'*x+3*(x)'))/((sin(3*x))^2))

(1/ctg(3*x))*((-(0*x+3*(x)'))/((sin(3*x))^2))

(1/ctg(3*x))*((-(0*x+3*1))/((sin(3*x))^2))

(1/ctg(3*x))*(-3/((sin(3*x))^2))

(-3/((sin(3*x))^2))/ctg(3*x)

The calculation above is a derivative of the function f (x)

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