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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: diffrentiate wrt to x.........
Forum Index -> Differential Calculus like the article? email it to a friend.  
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[Post New]17 Apr 2008 17:01:28 IST
    Subject: diffrentiate wrt to x.........
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zeeshanp (147)

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tan-1(sqrt(1+ x2) - 1)
...............x
       



da this things inside da tan inverse operation is divided by x...........what shud i substitute x for  to get da answer?

pls dont read da dots also............
i can feel the light betray me...............
not a single second left..........
    
[Post New]17 Apr 2008 17:15:01 IST
    Subject: Re:diffrentiate wrt to x.........
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sboosy (3063)

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\tan^{-1}(\frac{\sqrt{1+x^2}-1}{x}) \\ \\ \mbox{Put x} = \tan(\theta) \\ \\ \mbox{We get} \ \tan^{-1}(\frac{\sec(\theta)-1}{\tan(\theta)}) = \tan^{-1}(\frac{1-\cos(\theta)}{\sin(\theta)}) \\ \\ =\tan^{-1}(\frac{2\sin^2(\frac{\theta}{2})}{2\sin(\frac{\theta}{2})\cos(\frac{\theta}{2})}) = \tan^{-1} (\tan(\frac{\theta}{2})) = \frac{\theta}{2} \\ \\ =\frac{1}{2} \tan^{-1}x \\ \\ \mbox{Differentiating with respect to x we get} \\ \\ \frac{1}{2(1+x^2)}
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[Post New]17 Apr 2008 17:20:49 IST
    Subject: diffrentiate wrt to x.........
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sriram.a (222)

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yes your ans is correct
<SRIRAM.A> on high way of IIT




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