NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 71
Total: 72
x
1+tanx
Solution:  
Let f (x) =
x
1+tanx

⇒ f (x) = x(1+tanx)1 ... (i)
Differentiating (i) with respect to x, we get
d
dx
[f (x)] = 1 . (1+tanx)1 + x(sec2x)(1)(1+tanx)2
= (1+tanx)1 - x(sec2x)(1+tanx)2
=
1
1+tanx
xsec2x
(1+tanx)2

=
1+tanxxsec2x
(1+tanx)2

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