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Sponsor Area

Continuity And Differentiability

Question
CBSEENMA12034841

<pre>uncaught exception: <b>file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/64/ea/07693cdc340768600ec4c104b639.ini): failed to open stream: Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php at line #12file_put_contents(/home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/web/../../../../../../formulas/64/ea/07693cdc340768600ec4c104b639.ini): failed to open stream: Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php line 12<br />#0 [internal function]: _hx_error_handler(2, 'file_put_conten...', '/home/config_ad...', 12, Array)
#1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/sys/io/File.class.php(12): file_put_contents('/home/config_ad...', 'mml=<math xmlns...')
#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(48): sys_io_File::saveContent('/home/config_ad...', 'mml=<math xmlns...')
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(112): com_wiris_util_sys_Store->write('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
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#7 {main}</pre>

Solution
Here space space space straight y equals straight a to the power of xy
therefore space log space straight y equals log space straight a to the power of xy space space space space space space space space space space space space space space space space space space rightwards double arrow space log space straight y equals left square bracket xy right square bracket log space straight a
Differentiate space straight w. straight r. straight t. straight x comma
space space space space space space 1 over straight y dy over dx equals open square brackets straight x. dy over dx plus straight y.1 close square brackets log space straight a
therefore space space 1 over straight y dy over dx equals straight x space log space straight a dy over dx plus straight y space log space straight a space space space space space rightwards double arrow space space space space space space open parentheses 1 over straight x minus straight x space log space straight a close parentheses dy over dx equals straight y space log space straight a
rightwards double arrow space space space open parentheses fraction numerator 1 minus xy space log space straight a over denominator straight y end fraction close parentheses dy over dx equals straight y space log space straight a space space space space space rightwards double arrow space space space space space space dy over dx equals fraction numerator straight y squared log space straight a over denominator 1 minus xy space log space straight a end fraction

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