Question

Найти значение производной функции

Answer 1

Ответ:

Пошаговое объяснение:

resheno

Answer 2

Ответ:

$f(x)=\dfrac{sin(\pi x)}{ln(ex^2)}\ \ ,\ \ x_0=1\ \ ,\\\\\\f'(x)=\dfrac{\pi \cdot cos(\pi x)\cdot ln(ex^2)-sin(\pi x)\cdot \dfrac{2ex}{ex^2}}{ln^2(ex^2)}=\\\\\\=\dfrac{\pi \cdot cos(\pi x)\cdot ln(ex^2)-\dfrac{2}{x}\cdot sin(\pi x)}{(lne+lnx^2)^2}=\dfrac{\pi x\cdot cos(\pi x)\cdot (1+lnx^2)-2\, sin(\pi x)}{x\cdot (1+lnx^2)^2}$

$f'(1)=\dfrac{\pi \cdot cos\pi \cdot (1+ln1^2)-2\, sin\pi }{1\cdot (1+ln1^2)^2}=\dfrac{-\pi \cdot (1+0)-2\cdot 0}{(1+0)^2}=-\pi$