Derivative of ln x / e^x

Derivative of ln x / e^x

y = ln x/e^x

y = ln x * e^-x

dy/dx = -ln x * e^ -x + (e^-x)/x

dy/dx = e^ -x [-ln x + 1/x]

f ` (x) is given by Quotient Rule :-

(e^x) (1/x) - (ln x) (e^x)
--------------------------------------…
e^(2x)

e^x - x (lnx)(e^x)
------------------------
x e^(2x)

e^x ( 1 - x ln x )
--------------------------
xe^(2x)

1 - x ln x
------------
x e^x

d/dx [lnx / e^x] = 1/x * e^-x + - e^-x * ln(x)

= [e^-x]/x - [e^-x *ln(x)]