f'(x) = [tex]e^{-x}[/tex] / x - [tex]e^{-x}[/tex]lnx
Differentiate using the product rule
given f(x) = g(x)h(x) then
f'(x) = g(x)h'(x) + h(x)g'(x) ← product rule
g(x) = [tex]e^{-x}[/tex] ⇒ g'(x) = - [tex]e^{-x}[/tex]
h(x) = lnx ⇒ h'(x) = [tex]\frac{1}{x}[/tex]
f'(x) = [tex]e^{-x}[/tex].[tex]\frac{1}{x}[/tex] - [tex]e^{-x}[/tex]lnx
= [tex]e^{-x}[/tex] / x - [tex]e^{-x}[/tex]lnx
