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Given that $f^{ \prime }\left( x \right) =x\sin { \left( { x }^{ 2 } \right) }$ and $f\left( 0 \right) =\cfrac { 3 }{ 2 } $, find $f\left( \sqrt { \cfrac { \pi }{ 2 } } \right) $.

A

$-\cfrac { 3 }{ 2 } $

B

$0$

C

$\sqrt { \cfrac { \pi }{ 2 } } $

D

$2$

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