Derivative of ln((sin(x)*e^x)/ln(x))

Derivative of ln((sin(x)*e^x)/ln(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(x)*e^x)/ln(x)): 


(ln((sin(x)*e^x)/ln(x)))'

(1/((sin(x)*e^x)/ln(x)))*((sin(x)*e^x)/ln(x))'

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

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

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

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

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

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

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

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

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