sin(cosπx) найти производную, с объяснениями. Created by Coolyar. algebra-ru

sin(cosπx) найти производную, с объяснениями...

Coolyar @Coolyar

July 2022 1 8 Report

sin(cosπx) найти производную, с объяснениями

Answers & Comments

Miroslava227

Ответ:

$y = \sin( \cos(\pi \: x) )$

$y' = ( \sin( \cos(\pi \: x) )' \times ( \cos(\pi \: x))' \times (\pi \: x) '= \\ = \cos( \cos(\pi \: x) ) \times ( - \sin(\pi \: x)) \times \pi = \\ = - \pi \sin(\pi \: x) \times \cos( \cos(\pi \: x) )$

Это сложная функция, поэтому нужно взять производные еще от внутренних функций.

По формулам:

$( \cos(x))' = - \sin(x) \\ ( \sin(x))' = \cos(x) \\ (ax) '= a$

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