Question

Помогите срочноооо!!!!!!
sin 2x + sin 6x - cos 2x = 0
И вот ещё:
f(x) = ln (5x-4/2x-1) , f'(1)

Answer 1

$1); ; (sin2x+sin6x)-cos2x=0\\2sin4xcdot cos2x-cos2x=0\\cos2xcdot (2sin4x-1)=0\\cos2x=0; ,; 2x=frac{pi}{2}+pi n,; x=frac{pi}{4}+frac{pi n}{2}; ,; nin Z\\sin4x=frac{1}{2}; ,; 4x=(-1)^{m}frac{pi}{6}+pi m,; x=(-1)^{m}frac{pi}{24}+frac{pi m}{4}; ,; min Z\\2); ; f(x)=lnfrac{5x-4}{2x-1}\\f'(x)=frac{2x-1}{5x-4}cdot frac{5(2x-1)-2(5x-4)}{(2x-1)^2}= frac{2x-1}{5x-4} cdot frac{3}{(2x-1)^2} = frac{3}{(5x-4)(2x-1)} \\f'(1)=frac{3}{1cdot 1}=3$