Question

Найдите производную функций f(x)=cos^2 x/4-sin^2 x/4

Answer 1

$f(x)=cos^2\frac{x}{4}-sin^2\frac{x}{4}\\\\f'(x)=2cos\frac{x}{4}\cdot (-sin\frac{x}{4})\cdot \frac{1}{4}-2sin\frac{x}{4}\cdot cos\frac{x}{4}\cdot \frac{1}{4}=\\\\=-\frac{1}{2}\cdot (cos\frac{x}{4}\cdot sin\frac{x}{4}+sin\frac{x}{4}\cdot cos\frac{x}{4})=-\frac{1}{2}\cdot 2\cdot sin\frac{x}{4}\cdot cos\frac{x}{4}=\\\\=-\frac{1}{2}\cdot sin(2\cdot \frac{x}{4})=-\frac{1}{2}\cdot sin\frac{x}{2}$