A PHP Error was encountered

Severity: Notice

Message: Undefined variable: temp_qds

Filename: Questions_Page/Ncert_Question.php

Line Number: 320

Backtrace:

File: /home/wiredfa1/public_html/application/views/final/Questions_Page/Ncert_Question.php
Line: 320
Function: _error_handler

File: /home/wiredfa1/public_html/application/controllers/Home.php
Line: 235
Function: view

File: /home/wiredfa1/public_html/index.php
Line: 315
Function: require_once

Sponsor Area

Continuity And Differentiability

Question
CBSEENMA12035359

If space space straight y equals straight e to the power of straight x left parenthesis sin space straight x plus cos space straight x right parenthesis comma space prove space that space dy over dx minus 2 dy over dx plus 2 straight y equals 0

Solution
space space space space space space space space space space space space straight y equals straight e to the power of straight x left parenthesis sin space straight x plus cos space straight x right parenthesis
therefore space space dy over dx equals straight e to the power of straight x left parenthesis cos space straight x minus sin space straight x right parenthesis plus left parenthesis sin space straight x plus cos space straight x right parenthesis. straight e to the power of straight x
space space space space space space space space space space space space space space equals straight e to the power of straight x left parenthesis cos space straight x minus sin space straight x plus sin space straight x plus cos space straight x right parenthesis
therefore space space dy over dx equals 2 straight e to the power of straight x space cos space straight x
therefore space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 2 left square bracket straight e to the power of straight x left parenthesis negative sin space straight x right parenthesis plus cos space straight x. space straight e to the power of straight x right square bracket
therefore space fraction numerator straight d squared straight y over denominator dx squared end fraction equals 2 straight e to the power of straight x left parenthesis cos space straight x minus sin space straight x right parenthesis
straight L. straight H. straight S equals fraction numerator straight d squared straight y over denominator dx squared end fraction minus 2 dy over dx plus 2 straight y
space space space space space space space space space space space equals 2 e to the power of x left parenthesis cos space straight x minus sin space straight x right parenthesis minus 2 left parenthesis 2 e to the power of x space cos space straight x right parenthesis plus 2 e to the power of x left parenthesis sin space straight x plus cos space straight x right parenthesis
space space space space space space space space space space space equals 2 e to the power of x space cos space straight x minus 2 space e to the power of x space sin space straight x minus 4 space e to the power of x space cos space straight x plus 2 space e to the power of x space sin space straight x plus 2 space e to the power of x space cos space straight x
space space space space space space space space space space space equals 0 equals straight R. straight H. straight S.

Some More Questions From Continuity and Differentiability Chapter