F '(x) = ( tq(x/4 -x) =tq(-3x/4) = -tq3x/4 ;
f '(x) = ( -tq3x/4 )' = -(tq3x/4 )' = -(1/cos²3x/4) *(3x/4)' = -(1/cos²3x/4) *(3/4)*(x) '
= -(1/cos²3x/4) *(3/4)*(1) = -3/4cos²3x/4 * ** = - 3/2(1+cos3x/2).
f '(3π/4) = -3/4cos²(3*3π/4)/4 =-3/4cos²(9π/16)= -3/2(1+cos2*(9π/16) )=.
-3/2(1+cos9π/8) = -3/2(1+cos(π+π/8) ) = -3/2(1- cosπ/8) ,
но cosπ/8 =√((1+cosπ/4)/2) = √(1+(√2)/2)/2 = √(2+√2) /2 ,
окончательно : f '(3π/4) = -3/( 2-√(2+√2) ) .
* * * cosα =±√( (1+cos2α)/2 ) * * *