Derivative of ln(sin(3x)cos(x))

Derivative of ln(sin(3x)cos(x)). 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(sin(3x)cos(x)):


(ln(sin(3*x)*cos(x)))'

(1/(sin(3*x)*cos(x)))*(sin(3*x)*cos(x))'

(1/(sin(3*x)*cos(x)))*((sin(3*x))'*cos(x)+sin(3*x)*(cos(x))')

(1/(sin(3*x)*cos(x)))*(cos(3*x)*(3*x)'*cos(x)+sin(3*x)*(cos(x))')

(1/(sin(3*x)*cos(x)))*(cos(3*x)*((3)'*x+3*(x)')*cos(x)+sin(3*x)*(cos(x))')

(1/(sin(3*x)*cos(x)))*(cos(3*x)*(0*x+3*(x)')*cos(x)+sin(3*x)*(cos(x))')

(1/(sin(3*x)*cos(x)))*(cos(3*x)*(0*x+3*1)*cos(x)+sin(3*x)*(cos(x))')

(1/(sin(3*x)*cos(x)))*(3*cos(3*x)*cos(x)+sin(3*x)*(cos(x))')

(1/(sin(3*x)*cos(x)))*(3*cos(3*x)*cos(x)+sin(3*x)*(-sin(x)))

(3*cos(3*x)*cos(x)-(sin(x)*sin(3*x)))/(sin(3*x)*cos(x))

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

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