Differentiate $sin (x^{2} + 1)$

- 2 x sin (x^{2} + 1) .

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2 x cos (x^{2} + 1) .

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- 2 x cos (x^{2} + 1) .

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2 x sin (x^{2} + 1) .

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Solution

The correct option is C $2 x cos (x^{2} + 1) .$
Given, $y = sin (x^{2} + 1)$
let $t = x^{2} + 1$
$\frac{d y}{d x} = \frac{d y}{d t} \frac{d t}{d x}$
$∴ \frac{d y}{d x} = 2 x cos (x^{2} + 1)$
Hence, option B.

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