5.
$$y = \sec ^ { 2 } x$$
- Show that \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = 6 \sec ^ { 4 } x - 4 \sec ^ { 2 } x\).
- Find a Taylor series expansion of \(\sec ^ { 2 } x\) in ascending powers of \(\left( x - \frac { \pi } { 4 } \right)\), up to and including the term in \(\left( x - \frac { \pi } { 4 } \right) ^ { 3 }\).