tex]...

ViktorC @ViktorC

August 2022 1 10 Report

870) Найти производную данной функции и упростить ее:
[tex]y=\frac{sin x-xcos x}{cos x+xsin x}[/tex]

Answers & Comments

Artem112

Verified answer

$y=\frac{\sin x-x\cos x}{\cos x+x\sin x}$
$y'=\frac{(\sin x-x\cos x)'(\cos x+x\sin x)-(\sin x-x\cos x)(\cos x+x\sin x)'}{(\cos x+x\sin x)^2} =
\\\
=\frac{(\cos x-(\cos x-x\sin x))(\cos x+x\sin x)-(\sin x-x\cos x)(-\sin x+(\sin x+x\cos x))}{(\cos x+x\sin x)^2}=
\\\
=\frac{(\cos x-\cos x+x\sin x)(\cos x+x\sin x)-(\sin x-x\cos x)(-\sin x+\sin x+x\cos x)}{(\cos x+x\sin x)^2}=$
$=\frac{x\sin x(\cos x+x\sin x)-x\cos x(\sin x-x\cos x)}{(\cos x+x\sin x)^2}=
\\\
=\frac{x\sin x\cos x+x^2\sin^2 x-x\sin\cos x+x^2\cos^2x}{(\cos x+x\sin x)^2}=
\\\
=\frac{x^2(\sin^2 x+\cos^2x)}{(\cos x+x\sin x)^2}=\frac{x^2}{(\cos x+x\sin x)^2}$

1 votes Thanks 1

More Questions From This User See All

ViktorC August 2022 | 0 Ответы

tex]...

ViktorC August 2022 | 0 Ответы

tex]...

ViktorC August 2022 | 0 Ответы

tex]...

ViktorC August 2022 | 0 Ответы

tex najdite ordinatu toj tochki v kotoroj kasatelnaya k etomu grafiku obrazuet

ViktorC July 2022 | 0 Ответы

m3adecda10156d8e0fa495d00c0b928133 39777

ViktorC July 2022 | 0 Ответы

295 najti korni uravneniya a x2 4x1 410

ViktorC July 2022 | 0 Ответы

292 najti korni uravneniya a 2x2 3x1x2x 2

ViktorC July 2022 | 0 Ответы

293 najti korni uravneniya a x23x 13x

ViktorC July 2022 | 0 Ответы

tex]...

ViktorC July 2022 | 0 Ответы

tex]...

рекомендуемые вопросы

rarrrrrrrr August 2022 | 0 Ответы

o chem dolzhny pozabotitsya v pervuyu ochered vzroslye pri organizacionnom vyvoze n

danilarsentev August 2022 | 0 Ответы

est dva stanka na kotoryh vypuskayut odinakovye zapchasti odin proizvodit a zapcha

myachina8 August 2022 | 0 Ответы

najti po grafiku otnoshenie v3v1 v otvetah napisano 9 no nuzhno reshenie

ydpmn7cn6w August 2022 | 0 Ответы

Choose the correct preposition: 1.I am fond (out,of,from) literature. 2.where ar...

millermilena658 August 2022 | 0 Ответы

opredelite kak sozdavalas i kto sozdaval arabskoe gosudarstvo v kracii

MrZooM222 August 2022 | 0 Ответы

ch ajtmanov v rasskaze krasnoe yabloko ispolzuet metod rasskaz v rasskaze opi

timobila47 August 2022 | 0 Ответы

kakovo bylo naznachenie kazhdoj iz chastej vizantijskogo hrama pomogite pozhalujsta

ivanyyaremkiv August 2022 | 0 Ответы

pozhalujsta8b98a56c0152a07b8f4cbcd89aa2f01e 97513

sarvinozwakirjanova August 2022 | 0 Ответы

pomogite pozhalusto pzha519d7eb8246a08ab0df06cc59e9dedb 6631

Helpful Links

Политика конфиденциальности

Правила и условия

Контакты

Helpful Social

Copyright © 2024 SCHOLAR.TIPS - All rights reserved.