Question

Let y=lnx/e^x. Find the first and second derivative,

Answer 1

u = lnx --> u' = ...?
v = e^x --> v' = ....?
Using quotient rule

Answer 2

\[\frac{ \frac{ 1 }{ x } e^x-e^x(\ln(x))}{ e^2x }\]

Answer 3

divided by \[e^{2x}\]

Answer 4

=\[\frac{ 1/x-\ln(x) }{ e^2 }\]

Answer 5

second derivative
\[\frac{ (\frac{ -1 }{ x^2 }-\frac{ 1 }{ x })(e^2) -0}{ e^4 }\]

Answer 6

=\[ \frac{ -x-x^2 }{ x^3e^2 } \]