NIMCET 2013 Question Paper with solutions

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Question : 13 of 120

Marks: +1, -0

If f (x) =

tan^{-1}[{sinx}/{1+cosx}]

, then what is the first derivative of

f (x)

?

1/2
- 1/2
2
- 2

Solution:

Given,

f(x)=\tan^{-1}[{\sin x}/{1+\cos x}]

⇒f(x)=\tan^{-1}[\;\;{2\sin x{/}2\cos x{/}2}/{2\cos^{2}x{/}2}]

⇒f(x)=\tan^{-1}[\;{\sin x{/}2}/{\cos x{/}2}]

⇒f(x)=\tan^{-1}[\tan x{/}2]⇒f(x)=x/2

∴f'(x)=1/2

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