Question

а) f´ (х), если f(x)=3ln⁡√(cos⁡2x ) ...........................................................................Найти: б) f´ (9), если f(x)=1/7 (x-9)^7 *cos⁡2πx-1/π cos^2⁡ (π/4 )x

Answer 1

A) f'(x) = 3/√(Cos2x) * 1/2√Cos2x) *(-Sin2x) * 2 = --3Sin2x/Cos2x = -3tg2x
б) f'(x) = ( 1/7 * (x-9)^7* Сos2πx)' - (1/πCos³πx/4)'=
= (x-9)^6 * Cos2πx + 1/7 * (x-9)^7 * (-Sin2πx) * (-2) +2Cos^-1 πx/4* (-Sinπx/4 )* π/4.
f'(9) = Cos18π - π/2 Sin9π/4 /Cos9π/4= 1 - π/2