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Question

Differentiate the following w.r.to x
tan11x1+x

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Solution



let y=tan11+x21+x2
letx=cos2θdx=2sin2θ dθdx=11x2
1x=1cos2θ
=2sin2θ
1+x=1+cos2θ
=2cos2θ

1x1+x=tan2θ1+x21+x2=tanθ
y=tan11+x21+x2
=tan1(tanθ)
=0
dydx=dθdx=121x2


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