51²-41²= 63²-53²= 117²-17²= 164²-64²= 125²-25²= 14²-86²= 37²-63²= 81²-19²= 77²-23²= 68²-32²= 55²-53²= 41²-21²= 35²-55²= 22²-42²=

51²-41²=(51-41)*(51+41)=10*92=92063²-53²=(63-53)*(63+53)=10*116=1160117²-17²=(117-17)*(117+17)=100*134=13400164²-64²=(164-64)*(164+64)=100*228=2280125²-25²=(125-25)*(125+25)=100*150=1500014²-86²=(14-86)*(14+86)=(-72)*100=-720037²-63²=(37-63)*(37+63)=(-26)*100=-260081²-19²=(81-19)*(81+19)=62*100=620077²-23²=(77-23)*(77+23)=54*100=540068²-32²=(68-32)*(68+32)=36*100=360055²-53²=(55-53)*(55+53)=2*108=21641²-21²=(41-21)*(41+21)=20*62=124035²-55²=(35-55)*(35+55)=(-20)*90=-180022²-42²=(22-42)*(22+42)=(-20)*64=-1280

1)педставим sin2x=a

3a^2+10a+3=0

a=-3

a=-1/3

перейдем к исходным данным

sin2x=-3

sin2x=-1/3

по формуле дорешаешь

 

1) y=2sin(4x)-8cos(x/4)+(1/2)*tg(/12)*ctg(6x)

      y ' =8cos(4x)+2sin(x/4)+1/cos^2(x)+sin^2(x)/2

 

2) y=sin(x/4)+12cos(x/3)-10tg(x/2)+5ctg(2x)

      y ' = cos(x/4)/4-sin(x/3)/3-5/cos^2(x/2)+2*sin^2(2x)/5

 

3) y=(8/12)*sin(3x//3)*cos(3x/4)-40ctg(x/5)-tg(8x)

      y ' = (1/2)*sin(3x/4)+sin(3x/4)+8/sin^2(x)-8/cos^2(x)

 

4) y =cos(2x)*x^5

      y ' =-2sin(2x)*x^5+5cos(2x)*x^4

5) y=sin(2x)/cos(4x)

      y ' =2cos(2x)/cos(4x)+4sin(2x)/cos^2(4x)

 

6) y=8cos(4x-pi/3)

    y ' =-32sin(4x-pi/3)

 

7) y=10x^5+7x^4-8x^3+4/x-9sqrt(x)-4x+1,1

      y ' = 50x^4+28x^3-24x^2-4/x^2-9/2*sqrt(x)-4

 

8) y=sin(3x)*tg(3x)

      y ' = 3cos(3x)*tg(3x)+sin(3x)*3/cos^2(3x)

 

9) y=5x^6+2x^3+6x^2-6x-8

      y ' = 30x^5+6x^2+12x-6

      y '' = 150x^4+12x+12

 

10) y=4sin(2x)-16cos(4/x)

        y ' = 8cos(2x)+64sin(x/4)/x^2

        y '' =-16sin(2x) +16cos(x/4)/x^2-128sin(x/4)/x^3