Find the derivative of the following : from Mathematics Limits
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    Limits and Derivatives

    Multiple Choice QuestionsShort Answer Type

    41. Find the derivative of the following :


    space space space space space space space space fraction numerator 2 over denominator straight x plus 1 end fraction minus fraction numerator straight x squared over denominator 3 straight x minus 1 end fraction
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    42. Find the derivative of the following :



    space space space space space space space fraction numerator 1 plus begin display style 1 over straight x end style over denominator 1 minus begin display style 1 over straight x end style end fraction

    Let 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 straight y space equals space space fraction numerator 1 plus begin display style 1 over straight x end style over denominator 1 minus begin display style 1 over straight x end style end fraction equals fraction numerator begin display style fraction numerator straight x plus 1 over denominator straight x end fraction end style over denominator begin display style fraction numerator straight x minus 1 over denominator straight x end fraction end style end fraction equals fraction numerator straight x plus 1 over denominator straight x end fraction straight x fraction numerator straight x over denominator straight x minus 1 end fraction equals fraction numerator straight x plus 1 over denominator straight x minus 1 end fraction

    Differentiating both sides w.r.t.   x, we  get

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

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    43. 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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    44. Find the derivatives of the following :

    (ax+b)n (cx+ d)n 
    114 Views
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    45. Derivative of xn.
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    46.

    Derivative of (ax + b)n, n being a rational number.

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    47. Derivative of sin x :
    106 Views
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    48. Find the derivatives of the following functions :

    x100 
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    49. Find the derivatives of the following functions :

    6x100 - x55 + x
    139 Views
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    50. Find the derivatives of the following functions :

    space space space fraction numerator 1 over denominator square root of straight x end fraction
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