Answer
\[f''(\frac{π}{4})=3\sqrt{2}\]
Work Step by Step
\[f(t)=\sec t\]
Differentiate both side with respect to $t$
\[f'(t)=\sec t\:\tan t\]
Again ,differentiate both side with respect to $t$ using product rule
\[f''(t)=(\sec t)'\tan t+(\tan t)'\sec t\]
\[f''(t)=\sec t\:\tan^2 t+\sec ^3 t\]
\[f''(t)=\sec t(\:\tan^2 t+\sec ^2 t)\]
\[f''(\frac{π}{4})=\sec( \frac{π}{4})\left[\tan^2(\frac{π}{4})+\sec ^2(\frac{π}{4})\right]\]
\[f''(\frac{π}{4})=\sqrt{2}[1+2]\]
\[f''(\frac{π}{4})=3\sqrt{2}\]
Hence, \[f''(\frac{π}{4})=3\sqrt{2}.\]
