+91-8076753736 support@wiredfaculty.com
logo
logo

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
CBSEENMA12035442
Wired Faculty App

If space straight x squared over straight a squared plus straight y squared over straight b squared equals 1 comma space show space that space fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative fraction numerator straight b 4 over denominator straight a squared straight y cubed end fraction.

Solution
We space have space straight x squared over straight a squared plus straight y squared over straight b squared equals 1 Differentiating space botth space sides space of space left parenthesis 1 right parenthesis space straight w. straight r. straight t. straight x comma space we space get comma space fraction numerator 2 straight x over denominator straight a squared end fraction plus fraction numerator 2 straight y over denominator straight b squared end fraction dy over dx equals 0 comma space space space therefore space fraction numerator 2 straight y over denominator straight b 2 end fraction dy over dx equals negative fraction numerator 2 straight x over denominator straight a squared end fraction therefore space dy over dx equals negative straight b squared over straight a squared. straight x over straight y Again space differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space eget comma space space space space space fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative straight b squared over straight a squared open square brackets fraction numerator straight y.1 minus straight x. begin display style dy over dx end style over denominator straight y squared end fraction close square brackets equals negative fraction numerator straight b squared over denominator straight a squared straight y squared end fraction open square brackets straight y minus straight x dy over dx close square brackets space space space space space space space space space space space space space space equals negative fraction numerator straight b squared over denominator straight a squared straight y squared end fraction open square brackets straight y minus straight x. open parentheses negative straight b squared over straight a squared straight x over straight y close parentheses close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket because space of space left parenthesis 2 right parenthesis right square bracket therefore space fraction numerator straight d squared straight y over denominator dx squared end fraction equals fraction numerator straight b squared over denominator straight a squared straight y squared end fraction open square brackets straight y plus straight b squared over straight a squared straight x squared over straight y close square brackets equals negative fraction numerator straight b squared over denominator straight a squared straight y squared end fraction. straight b squared over straight y open square brackets straight y squared over straight b squared plus straight x squared over straight a squared close square brackets equals negative fraction numerator straight b to the power of 4 over denominator straight a squared straight y cubed end fraction.1 therefore space fraction numerator straight d squared straight y over denominator dx squared end fraction equals negative fraction numerator straight b to the power of 4 over denominator straight a squared straight y cubed end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space left square bracket because space of space left parenthesis 2 right parenthesis right square bracket

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation