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Question

If y=tan1[2x1+2x+1],<x< then dydx at x=0 is

A
35ln 2
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B
110ln 2
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C
2
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D
None of these
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Solution

The correct option is B 110ln 2
We know that ddx(tan1x)=11+x2 , but in this case the argument of tan1x is a different function of x and not x itself. So we will apply chain rule.
y=tan12x1+2x+1
dydx=11+[2x1+2x+1]2×ddx(2x1+2x+1) [Using chain rule]
=11+[2x1+2x+1]2×2x ln2(1+2x+1)2x×2x+1ln2(1+2x+1)2 [Using quotient rule]
Put x=0 to get dydxx=0=110ln2 which is the correct answer

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