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If $f (x) = \int_{1 / x^{2}}^{x^{2}} \cos \sqrt{t} d t,$ then $f^{'} (1)$ is equal to

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cos 1

2 cos 1

4 cos 1

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Correct option is C

f′(x)=cos⁡ x2ddxx2−cos⁡ 1/x2ddx1x2 (Using Property 18)=2xcos⁡x+2x3cos⁡(1/x). Hence f′(1)=4cos⁡ 1.

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If f(x)=∫1/x2x2 cos⁡ tdt, then f′(1) is equal to

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If $f (x) = \int_{1 / x^{2}}^{x^{2}} \cos \sqrt{t} d t,$ then $f^{'} (1)$ is equal to