15.
$$y = \cosh ^ { n } x \quad n \geqslant 5$$
- Show that
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = n ^ { 2 } \cosh ^ { n } x - n ( n - 1 ) \cosh ^ { n - 2 } x$$
- Determine an expression for \(\frac { \mathrm { d } ^ { 4 } y } { \mathrm {~d} x ^ { 4 } }\)
- Hence, or otherwise, determine the first three non-zero terms of the Maclaurin series for \(y\), simplifying each coefficient and justifying your answer.
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