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: $frac{-1}{pi}.$