- The curve \(C\) has equation \(y = \mathrm { g } ( x )\) where
$$g ( x ) = e ^ { 3 x } \sec 2 x \quad - \frac { \pi } { 4 } < x < \frac { \pi } { 4 }$$
- Find \(\mathrm { g } ^ { \prime } ( x )\)
- Hence find the \(x\) coordinate of the stationary point of \(C\).
(ii) A different curve has equation
$$x = \ln ( \sin y ) \quad 0 < y < \frac { \pi } { 2 }$$
Show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { \mathrm { e } ^ { x } } { \mathrm { f } ( x ) }$$
where \(\mathrm { f } ( x )\) is a function of \(\mathrm { e } ^ { x }\) that should be found.
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |