Question

What id the devirative of

`f(x) = e {}^( - x) ln(x)`

Answer 1

f'(x) =
`e^(-x)` / x -
`e^(-x)`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) =
`e^(-x)` ⇒ g'(x) = -
`e^(-x)`

h(x) = lnx ⇒ h'(x) =
`(1)/(x)`

f'(x) =
`e^(-x)`.
`(1)/(x)` -
`e^(-x)`lnx

=
`e^(-x)` / x -
`e^(-x)`lnx