Differentiate the following functions w.r.t. x from Mathematics
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    Limits and Derivatives

    Multiple Choice QuestionsShort Answer Type

    51.

    Find the derivative of space space space straight y space equals space 10 to the power of 10 plus 10 over straight x plus straight x over 10 plus 10 straight x plus straight x to the power of 10

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    52.

    Find the derivative of (2x+3)(5x2-7x+1)

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    53. Differentiate the following functions w.r.t. x


    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 fraction numerator straight x minus 1 over denominator 3 straight x cubed plus 2 end fraction comma space straight x space not equal to space cube root of fraction numerator negative 2 over denominator 3 end fraction end root

    Let     space space space space space space space space space space space space space space space space space space space space space straight f left parenthesis straight x right parenthesis space equals space fraction numerator straight x minus 1 over denominator 3 straight x cubed plus 2 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 straight f left parenthesis straight x right parenthesis space space equals space fraction numerator left parenthesis 3 straight x cubed plus 2 right parenthesis begin display style straight d over dx end style left parenthesis straight x minus 1 right parenthesis minus left parenthesis straight x minus 1 right parenthesis begin display style straight d over dx end style left parenthesis 3 straight x cubed plus 2 right parenthesis over denominator open parentheses 3 straight x cubed plus 2 close parentheses squared end fraction        (By Quotient Rule)

              space space space space space space space space space space space space space space space space space space space equals space space space space fraction numerator left parenthesis 3 straight x cubed plus 2 right parenthesis left parenthesis 1 minus 0 right parenthesis minus left parenthesis straight x minus 1 right parenthesis left parenthesis 9 straight x squared plus 0 right parenthesis over denominator left parenthesis 3 straight x cubed plus 2 right parenthesis squared end fraction equals fraction numerator 3 straight x cubed plus 2 minus 9 straight x cubed plus 9 straight x squared over denominator left parenthesis 3 straight x cubed plus 2 right parenthesis squared end fraction


                    space space space space space space space space space space space space space equals space space fraction numerator negative 6 straight x cubed plus 9 straight x squared plus 2 over denominator left parenthesis 3 straight x cubed plus 2 right parenthesis squared end fraction


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    54.

    Solve   space space space space space space space space space space limit as straight z rightwards arrow 1 of fraction numerator straight z to the power of begin display style 1 third end style end exponent minus 1 over denominator straight z to the power of begin display style 1 over 6 end style end exponent minus 1 end fraction

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    55.

    If <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /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...') #4 /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) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>,  find n.

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    56.

    Evaluate  <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /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...') #4 /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) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>

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    57. Differentiate the following functions w.r.t. x


    space space space space space space space space space space space space fraction numerator left parenthesis straight x plus 2 right parenthesis left parenthesis 1 minus 3 straight x right parenthesis over denominator 2 straight x plus 1 end fraction semicolon space space straight x space not equal to space fraction numerator negative 1 over denominator 2 end fraction
    124 Views
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    58. Find the derivatives of the following :



    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /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...') #4 /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) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
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    59. Find the derivatives of the following :



    space space space space space space space space space space fraction numerator 3 straight x plus 2 over denominator left parenthesis straight x plus 5 right parenthesis left parenthesis 2 straight x plus 1 right parenthesis plus 3 end fraction
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    60. Find the derivatives of the following :


    <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /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...') #4 /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) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
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