A) \[\sin {{x}^{2}}-\sin x\]
B) \[4{{x}^{3}}\sin {{x}^{2}}-2x\sin x\]
C) \[{{x}^{4}}\sin {{x}^{2}}-x\sin x\]
D) None of these
Correct Answer: B
Solution :
We have \[f(x)=\int_{{{x}^{2}}}^{{{x}^{4}}}{\sin \sqrt{t}}\,dt\] \\[f'(x)=\frac{d}{dx}({{x}^{4}})(\sin \sqrt{{{x}^{4}}})-\frac{d}{dx}({{x}^{2}})\,(\sin \sqrt{{{x}^{2}}})\] \[=4{{x}^{3}}\sin {{x}^{2}}-2x\sin x\].
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