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Limits and Derivatives

Short Answer Type

71.

Find the derivatives of the following functions :

5 sec x + 4 cos x

274 Views

72.

Find the derivatives of the following functions :

sin x cos x

123 Views

73.

Find the derivatives of the following functions :

2 tan x - 7 sec x

114 Views

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

104 Views

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)

131 Views

77. Find the derivatives of the following functions :

Let $space space space space space space space space space space space space space space space straight y space equals space fraction numerator straight x squared cos open parentheses begin display style straight pi over 4 end style close parentheses over denominator sin space straight x end fraction space equals space space cos open parentheses straight pi over 4 close parentheses straight x squared cosec space straight x$

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

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$space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space straight x space cos open parentheses straight pi over 4 close parentheses cosec space straight x space left square bracket 2 minus straight x space cot space straight x right square bracket$

120 Views

78. Find the derivatives of the following functions :

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

104 Views

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

96 Views

80.

Evaluate the following limits :

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105 Views