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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

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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)

Let y = (x + sec x)(x - tan x)

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

$space space space space space space space space space space space space space space space space space space space space space space space space space space space space dy over dx equals space space left parenthesis straight x space plus space sec space straight x right parenthesis space straight d over dx left parenthesis straight x space minus space tan space straight x right parenthesis plus left parenthesis straight x space minus space tan space straight x right parenthesis straight d over dx left parenthesis straight x plus sec space straight x right parenthesis$

$space space space space space space space space space space space space space space space space space space space equals space left parenthesis straight x plus sec right parenthesis space left parenthesis 1 plus space sec squared space straight x right parenthesis plus left parenthesis straight x minus tan space straight x right parenthesis space left parenthesis 1 plus sec space straight x space tan space straight x right parenthesis$

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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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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

78. Find the derivatives of the following functions :(x + sec x)(x - tan x)

78. Find the derivatives of the following functions :

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