ddx(x2+1)n=n(x2+1)n−1ddx(x2+1) =n(x2+1)n−1(2x) =2xn(x2+1)n−1

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$\frac{d}{d x} {(x^{2} + 1)}^{n}$

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(n - 1) {(x^{2} + 1)}^{n - 1}

2 x n {(x^{2} + 1)}^{n - 1}

n {(x^{2} + 1)}^{n - 1}

2 x + {(x^{2} + 1)}^{n - 1}

answer is B.

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Detailed Solution

\frac{d}{d x} {(x^{2} + 1)}^{n} = n {(x^{2} + 1)}^{n - 1} \frac{d}{d x} (x^{2} + 1)

$= n {(x^{2} + 1)}^{n - 1} (2 x)$

$= 2 x n {(x^{2} + 1)}^{n - 1}$

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