найти производную функции: f(x) = 2x-1 / 2x +1 f(x)```=?. Created by AnnGoldy. algebra-ru

Ответ:Объяснение:Дана функция:Производные функции:

2x +1 f(x)```=?...

AnnGoldy @AnnGoldy

July 2022 1 3 Report

найти производную функции:

f(x) = 2x-1 / 2x +1

f(x)```=?

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Ответ:

$\tt \displaystyle f'''(x)=\frac{96}{(2 \cdot x+1)^{4}}$

Объяснение:

Дана функция:

$\tt \displaystyle f(x)=\frac{2 \cdot x-1}{2 \cdot x+1}$

Производные функции:

$\tt \displaystyle f'(x)=\left (\frac{2 \cdot x-1}{2 \cdot x+1} \right )'=\frac{(2 \cdot x-1)' \cdot (2 \cdot x+1)-(2 \cdot x-1) \cdot (2 \cdot x+1)'}{(2 \cdot x+1)^2} =\\\\=\frac{2 \cdot (2 \cdot x+1)-(2 \cdot x-1) \cdot 2}{(2 \cdot x+1)^2} =\frac{4 \cdot x+2-4 \cdot x+2}{(2 \cdot x+1)^2} =\frac{4}{(2 \cdot x+1)^2}$

$\tt \displaystyle f''(x)=\left (\frac{4}{(2 \cdot x+1)^2} \right )'=\left (4 \cdot (2 \cdot x+1)^{-2}} \right )'= \\\\= 4 \cdot (-2) \cdot (2 \cdot x+1)^{-2-1}} \cdot (2 \cdot x+1)'=-8 \cdot (2 \cdot x+1)^{-3}} \cdot 2=-16 \cdot (2 \cdot x+1)^{-3}}$

$\tt \displaystyle f'''(x)=\left (-16 \cdot (2 \cdot x+1)^{-3}} \right )'= -16 \cdot (-3) \cdot (2 \cdot x+1)^{-3-1}} \cdot (2 \cdot x+1)'=\\\\=48 \cdot (2 \cdot x+1)^{-4}} \cdot 2= 96\cdot (2 \cdot x+1)^{-4}} =\frac{96}{(2 \cdot x+1)^{4}} .$

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AnnGoldy August 2022 | 0 Ответы

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pomogite s resheniem zadachki po fizike cherez polozhenie materialnoj tochki kat

najdite ploshad polnoj poverhnosti pravilnoj chetyrehugolnoj prizmy esli dlinac282982d73c80ce687769ad4bf45044d 9118

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