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Composite Function

lf y=x2+1si...

Question

lf $y = (x^{2} + 1)^{s i n x}$ , then $y^{^{'}} (0)$ is equal to

A

\frac{1}{2}

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B

e^{2}

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C

0

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D

\frac{3}{2}

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Solution

The correct option is C $0$
$y^{'} (x) = (x^{2} + 1)^{sin x} (cos x l o g (1 + x^{2}) + sin x (\frac{2 x}{1 + x^{2}}))$
$y^{'} (0) = 1 (0 + 0)$
$= 0$

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