Derivative of (2*cos(e^(2*x))*e^(2*x))/sin(e^(2*x))

Derivative of (2*cos(e^(2*x))*e^(2*x))/sin(e^(2*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 (2*cos(e^(2*x))*e^(2*x))/sin(e^(2*x)): 


((2*cos(e^(2*x))*e^(2*x))/sin(e^(2*x)))'

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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