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Limits and Derivatives

Short Answer Type

71.

Find the derivatives of the following functions :

5 sec x + 4 cos x

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72.

Find the derivatives of the following functions :

sin x cos x

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73.

Find the derivatives of the following functions :

2 tan x - 7 sec x

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74. Find the derivatives of the following functions :

space space space space space space space space fraction numerator sec space straight x space minus 1 over denominator sec space straight x space plus 1 end fraction

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75. Find the derivatives of the following functions :

$space space space space fraction numerator sin left parenthesis straight x plus straight a right parenthesis over denominator cos space straight x end fraction$

Let y $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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

$space space space space space space space space space space space dy over dx equals straight d over dx left square bracket cos space straight a space tan space straight x space plus space sin space straight a right square bracket space equals space cos space straight a space straight d over dx tan space straight x space plus straight d over dx sin space straight a$

= cos a sec²x +0 = cos a sec²x

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76. Find the derivatives of the following functions :

(ax²+sin x) (p + q cos x)

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77. Find the derivatives of the following functions :

"<pre

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78. Find the derivatives of the following functions :

(x + sec x)(x - tan x)

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79. Find the derivatives of the following functions :

space space space space space space space space space space space space space space space space space space fraction numerator straight x over denominator 1 plus tan space straight x end fraction

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80.

Evaluate the following limits :

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105 Views