Y=2sin4x + cos4x; Найти y'' (pi/8);

y' = (2sin4x) ' + (cos4x) ' = 2cos4x * (4x) ' + ( - sin4x) * (4x) ' =

= 2cos4x * 4 - sin4x * 4 = 8cos4x - 4sin4x.

y'' = (8cos4x) ' - (4sin4x) ' = - 8sin4x * (4x) ' - 4cos4x * (4x) ' =

= - 8sin4x * 4 - 4cos4x * 4 = - 32sin4x - 16cos4x.

y'' (п/8) = - 32sin (4 * п/8) - 16cos (4 * п/8) = - 32sin (п/2) - 16cos (п/2) =

= - 32 * 1 - 16 * 0 = - 32.

Ответ: y'' (п/8) = - 32.