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
CBSEENMA12035029

Find space dy over dx when space straight x equals fraction numerator sin cubed straight t over denominator square root of cos space 2 straight t end root end fraction comma space straight y equals fraction numerator cos cubed straight t over denominator square root of cos space 2 straight t end root end fraction

Solution
space space space space space space straight x equals fraction numerator sin cubed straight t over denominator square root of cos space 2 straight t end root end fraction comma space space straight y equals fraction numerator cos cubed straight t over denominator square root of cos space 2 straight t end root end fraction
dx over dt equals fraction numerator square root of cos space 2 straight t end root.3 space sin squared straight t. begin display style fraction numerator negative 2 sin space 2 straight t over denominator 2 square root of cos space 2 straight t end root end fraction end style over denominator cos space 2 straight t end fraction
space space space space space space space space equals space fraction numerator begin display style fraction numerator 3 sin squared straight t space cos space straight t space square root of cos space 2 straight t space end root over denominator 1 end fraction end style plus begin display style fraction numerator sin cubed straight t space sin space 2 straight t over denominator square root of cos space 2 straight t end root end fraction end style over denominator cos space 2 straight t end fraction
space space space space space space space space equals fraction numerator begin display style 3 sin squared straight t space cos space straight t space. cos space 2 straight t plus sin cubed straight t space sin space 2 straight t end style over denominator open parentheses cos space 2 straight t close parentheses to the power of begin display style 3 over 2 end style end exponent end fraction
dy over dt equals fraction numerator square root of cos space 2 straight t end root. left parenthesis negative 3 cos squared straight t space sin space straight t right parenthesis minus cos cubed straight t. begin display style fraction numerator negative 2 sin space 2 straight t over denominator 2 square root of cos space 2 straight t end root end fraction end style over denominator cos space 2 straight t end fraction
space space space space space space space space equals fraction numerator negative begin display style fraction numerator 3 cos squared straight t space sin space straight t square root of cos space 2 straight t end root over denominator 1 end fraction end style plus begin display style fraction numerator cos cubed straight t space sin space 2 straight t over denominator square root of cos space 2 straight t end root end fraction end style over denominator cos space 2 straight t end fraction
dy over dt equals fraction numerator negative 3 cos squared straight t space sin space straight t space cos space 2 straight t plus cos cubed straight t space sin space 2 straight t over denominator open parentheses cos space 2 straight t close parentheses to the power of 3 over 2 end exponent end fraction
Now space dy over dx equals fraction numerator begin display style dy over dt end style over denominator begin display style dx over dt end style end fraction
equals fraction numerator negative 3 cos squared straight t space sin space straight t space cos space 2 straight t plus cos cubed straight t space sin space 2 straight t over denominator open parentheses cos space 2 straight t close parentheses to the power of 3 over 2 end exponent end fraction cross times fraction numerator open parentheses cos space 2 straight t close parentheses to the power of 3 over 2 end exponent over denominator 3 sin squared straight t space cos space straight t space. cos space 2 straight t plus sin cubed straight t space sin space 2 straight t end fraction
equals fraction numerator negative 3 cos squared straight t space sin space straight t space cos space 2 straight t plus cos cubed straight t space sin space 2 straight t over denominator 3 sin squared straight t space cos space straight t space. cos space 2 straight t plus sin cubed straight t space sin space 2 straight t end fraction
equals fraction numerator negative 3 cos squared straight t space sin space straight t left parenthesis 2 cos squared straight t minus 1 right parenthesis plus cos cubed straight t space.2 sin space straight t space cos space straight t over denominator 3 sin squared straight t space cos space straight t space left parenthesis 1 minus 2 sin squared straight t right parenthesis. negative plus 2 sin space straight t space cos space 2 straight t plus sin cubed straight t space end fraction
equals fraction numerator negative 6 cos to the power of 4 straight t space sin space straight t plus 3 space cos squared straight t space sin space straight t plus 2 sint space cos to the power of 4 straight t over denominator 3 sin squared straight t space cos space straight t minus 6 space sin to the power of 4 straight t space cos space straight t plus space 2 sin to the power of 4 straight t space cos space straight t end fraction equals fraction numerator negative 4 cos to the power of 4 straight t space sin space straight t plus 3 cos squared straight t space sin space straight t over denominator 3 sin squared straight t space cos space straight t minus 4 sin to the power of 4 straight t space cos space straight t end fraction
equals fraction numerator sin space straight t space cos space straight t left parenthesis 3 cos space straight t minus 4 cos cubed straight t right parenthesis over denominator negative sin space straight t space cos space straight t left parenthesis 4 sin cubed straight t minus 3 sint right parenthesis end fraction equals negative fraction numerator cos space 3 straight t over denominator sin space 3 straight t end fraction equals negative cot space 3 straight t.

Some More Questions From Continuity and Differentiability Chapter