Moderate -0.5 This is a straightforward application of the quotient rule to differentiate ln(x)/x², followed by direct substitution of x=e. The calculation is routine with no conceptual challenges—slightly easier than average due to the clean result when substituting e.
1 Given that \(y = \frac { \ln x } { x ^ { 2 } }\), find the exact value of \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(x = \mathrm { e }\).
1 Given that $y = \frac { \ln x } { x ^ { 2 } }$, find the exact value of $\frac { \mathrm { d } y } { \mathrm {~d} x }$ when $x = \mathrm { e }$.\\
\hfill \mbox{\textit{CAIE P2 2022 Q1 [3]}}