Derivative of ln(e^-2x/sin(4x))

Derivative of ln(e^-2x/sin(4x)). 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(e^-2x/sin(4x)): 


(ln((e^-2*x)/sin(4*x)))'

(1/((e^-2*x)/sin(4*x)))*((e^-2*x)/sin(4*x))'

(1/((e^-2*x)/sin(4*x)))*(((e^-2*x)'*sin(4*x)-(e^-2*x*(sin(4*x))'))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*((((e^-2)'*x+e^-2*(x)')*sin(4*x)-(e^-2*x*(sin(4*x))'))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*(((0*x+e^-2*(x)')*sin(4*x)-(e^-2*x*(sin(4*x))'))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*(((0*x+e^-2*1)*sin(4*x)-(e^-2*x*(sin(4*x))'))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*((e^-2*sin(4*x)-(e^-2*x*(sin(4*x))'))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*((e^-2*sin(4*x)-(e^-2*x*cos(4*x)*(4*x)'))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*((e^-2*sin(4*x)-(e^-2*x*cos(4*x)*((4)'*x+4*(x)')))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*((e^-2*sin(4*x)-(e^-2*x*cos(4*x)*(0*x+4*(x)')))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*((e^-2*sin(4*x)-(e^-2*x*cos(4*x)*(0*x+4*1)))/((sin(4*x))^2))

(1/((e^-2*x)/sin(4*x)))*((e^-2*sin(4*x)-(e^-2*x*4*cos(4*x)))/((sin(4*x))^2))

e^2*x^-1*(e^-2*sin(4*x)-(4*e^-2*x*cos(4*x)))*(sin(4*x))^-1

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

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