Question

Помогите по алгебре чем сможете. Даю 100 баллов.

Answer 1

$1)f(x)=2sqrt{3} Cos4x-2Cosx\f'(x)=2sqrt{3}(Cos4x)'- 2(Cosx)'=2 sqrt{3}*(-Sin4x)*(4x)'+2Sinx=-8 sqrt{3}Sin4x+2Sinx\\\f'( pi/6)=-8 sqrt{3}Sin(4* pi/6)+2Sin pi/6=-8 sqrt{3}Sin2 pi/3+2Sin pi/6=-8 sqrt{3}* frac{sqrt{3}} {2}+2* frac{1}{2}=-12+1=-11$

2) y = (- 10x - 5)⁷

y' = [(- 10x- 5)⁷]' = 7(- 10x - 5)⁶ * (- 10x - 5)' = 7(- 10x - 5)⁶ * (- 10) =

= - 70(- 10x - 5)⁶

$y=lntgx\y' = (lntgx)' = frac{1}{tgx} *(tgx)' = frac{1}{tgx} *frac{1}{Cos^{2}x}= frac{Cosx}{Sinx}* frac{1}{Cos^{2}x}= frac{1}{SinxCosx}= frac{2}{Sin2x} \y'(pi/12)= frac{2}{Sin(2*pi/12)}= frac{2}{Sinpi/6}= frac{2}{frac{1}{2}} =4$