16) f(x)=(9x+5)⁸
f(x)' =8(9x+5)⁷ * 9=72*(9x+5)⁷
17) f(x)=√(2x¹⁶+x³+6)
f(x)' = <u> 1 </u> * (32x¹⁵+3x²) = <u> 32x¹⁵+3x² </u>
2√(2x¹⁶+x³+6) 2√(2x¹⁶+x³+6)
18) f(x)= <u> 1 </u>
sinx
f(x)' = - <u> 1 </u>* (sinx)' = -<u> cosx</u>
sin²x sin²x
19) f(x)=cos6x
f(x)'=-6sinx
21) f(x)=(x¹¹-2x+3)⁶+8x²
f(x)' =6(x¹¹-2x+3)⁵ * (11x¹⁰-2)+16x=(66x¹⁰-12)(x¹¹-2x+3)⁵+8x²
.............................
1
sinx=1/2
x=(-1)^n*π/6+πn,n∈z
2
перейдем к основанию 2
(log(2)3+5):1/(log(2)3-1) -(log(2)3+3):1/(log(2)3+1)=
=(log(2)3+5)*(log(2)3-1) -(log(2)3+3)*(log(2)3+1)=
=log²(2)(3)-log(2)3+5log(2)3-5-log²(2)3-log(2)3-3log(2)3-3=-8
3
sina-cosa=0,5
sinacosa=[1-(sina-cosa)²]:2=(1-0,25):2=0,75:2=0,375
sin³a-cos³a=(sina-cosa)(sin²a+sinacosa+cos²a)=0,5*(1+0,375)=0,6875
4
log(32)log(2)(2^1/16)=log(3)(1/16)=-4/5=-0,8
5
sina-cosa=-0,25
sinacosa=[1-(sina-cosa)²]:2=(1-0,0625):2=0,9375:2=0,46875
32(sin³a-cos³a)=32(sina-cosa)(sin²a+sinacosa+cos²a)=
=32*(-0,25)*(1+0,46875)=-11,75
6
log(√a)9=2
2log(a)3/(0,5)=6log(a)3
6log(a)3=2
log(a)3=1/3
log(a)27=3log(a)3=3*1/3=1
7
t^(17/3):t^(8/3)=t^(17/3-8/3)=t²
8
-ctgx=√3
ctgx=-√3
x=5π/6+πn,n∈z