Hard +2.3 This AEA question requires recognizing an incorrect application of the chain rule (the given formula is wrong—it should be the product rule), then correctly applying the product rule to solve a differential equation with an initial condition. This demands strong conceptual understanding, error identification, and multi-step integration techniques beyond standard A-level.
3.Given that
$$\frac { \mathrm { d } } { \mathrm {~d} x } ( u \sqrt { } x ) = \frac { \mathrm { d } u } { \mathrm {~d} x } \times \frac { \mathrm { d } ( \sqrt { } x ) } { \mathrm { d } x } , \quad 0 < x < \frac { 1 } { 2 }$$
where \(u\) is a function of \(x\) ,and that \(u = 4\) when \(x = \frac { 3 } { 8 }\) ,find \(u\) in terms of \(x\) .
(9)
3.Given that
$$\frac { \mathrm { d } } { \mathrm {~d} x } ( u \sqrt { } x ) = \frac { \mathrm { d } u } { \mathrm {~d} x } \times \frac { \mathrm { d } ( \sqrt { } x ) } { \mathrm { d } x } , \quad 0 < x < \frac { 1 } { 2 }$$
where $u$ is a function of $x$ ,and that $u = 4$ when $x = \frac { 3 } { 8 }$ ,find $u$ in terms of $x$ .\\
(9)\\
\hfill \mbox{\textit{Edexcel AEA 2005 Q3 [9]}}