Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0000 360720 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0527 1209368 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0527 1209368 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1201 4036840 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1215 4064392 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1222 4082104 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1222 4099112 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1230 4106848 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1230 4106848 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1694 4346728 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1709 4364128 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1714 4385056 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.1803 4457248 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.1803 4457504 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182 Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0000 360720 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0527 1209368 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0527 1209368 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1201 4036840 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1215 4064392 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1222 4082104 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1222 4099112 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1230 4106848 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1230 4106848 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1694 4346728 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1709 4364128 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1714 4385056 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3080 12252200 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.3083 12252648 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.3083 12252648 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.3085 12260896 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.3087 12262632 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.3094 12295680 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.3094 12296080 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.3095 12296160 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

Differentiation - The Chain Rule

If we have to differentiate a function which consists of one operation carried out after another we have to use the chain rule. Several examples are shown below together with the constituent functions which we call u and v.

Function

We differentiateandand substitute them into The Chain Rule:

Example: Differentiate

Now just multiply the differentiated terms:

Our final answer must be in terms ofHence we substituteThe final answer is

Example:Differentiate e^(2x-1)

Now just multiply the differentiated terms:

Our final answer must be in terms ofHence we substituteThe final answer is

Example: Differentiate 1 over {x^2+2}

Now just multiply the differentiated terms:

Our final answer must be in terms ofHence we substituteThe final answer is

Add comment

Security code
Refresh