Question

second derivative {sec }

Answer 1

evaluate
\[\huge \sec''\frac{ \pi }{ 4 }+\sec ''\frac{ 3\pi }{ 4}+\sec''\frac{ 5\pi }{ 4 }+\sec'' \frac{ 7\pi }{ 4 }\]

Answer 2

\[\sec'' \text{means second derivative sec}\]

Answer 3

\[ \sec''(x) = \sec(x)(\sec^2(x) + \tan^2(x))\]

use \( \sec(\pi -x) = -\sec(x)\)
http://www.wolframalpha.com/input/?i=Sum%5Bsec%28%282k%2B1%29pi%2F4%29%28sec%5E2%28%282k%2B1%29pi%2F4%29+%2B+tan%5E2%28%282k%2B1%29pi%2F4%29%29%2C%7Bk%2C+0%2C+3%7D%5D