Question

Найти значение производной функции f(x) в точке x0

f (x)=sin (1 - x/Пи)

x0=Пи

Answer 1

f(x) = sin(1 - x/π)

f'(x) = (sin(1 - x/π))' = (1 - x/π)'sin'(1 - x/π) = -cos(1 - x/π)/π

f'(x0) = f'(π) = -cos(1 -1)/π = -cos(0)/π = -1/π

Answer 2

$f(x)=\sin{(1-\frac{x}{\pi})}\\\\f'(x)=\cos{(1-\frac{x}{\pi})}\cdot (1-\frac{1}{\pi}\cdot x)'\\\\=\cos{(1-\frac{x}{\pi})}\cdot (0-\frac{1}{\pi}\cdot 1)=\-\frac{\cos{(1-\frac{x}{\pi})}}{\pi}\\\\f'(\pi)=-\frac{\cos{(1-\frac{\pi}{\pi})}}{\pi}=-\frac{\cos 1-1}{\pi}=-\frac{1}{\pi}$

Ответ: $\frac{-1}{\pi}.$