1) y=2sin(4x)-8cos(x/4)+(1/2)*tg(2x)-(1/12)*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/4)-(4/3)*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
tg²x=a
a+3/a=4
a²-4a+3=0
a1+a2=4 U a1*a2=3
a1=1⇒tg²x=1⇒tgx=-1 U tgx=1
x1=-π/4+πn,n∈z
-π<-π/4+πn<π
-4<-1+4n<4
-3<4n<5
-3/4<n<5/4
n=0⇒x=-π/4
n=1⇒x=-π/4+π=3π/4
x2=π/4+πk,k∈z
-π<π/4+πk<π
-4<1+4k<4
-5<4k<3
-5/4<k<3/4
k=-1⇒x=π/4-π=-3π/4
k=0⇒x=π/4
a2=3⇒tg²x=3⇒tgx=-√3 U tgx=√3
x3=-π/3+πm,m∈z
-π<-π/3+πm<π
-3<-1+3m<3
-2<3m<4
-2/3<m<4/3
m=0⇒x=-π/3
m=1⇒x=-π/3+π=2π/3
x4=π/3+πl,l∈z
-π<π/3+πl<π
-3<1+3l<3
-4<3l<2
-4/3<l<2/3
l=-1⇒x=π/3-π=-2π/3
l=0⇒x=π/3