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Câu hỏi: Hàm số $f\left( x \right)={{\cos }^{2}}\left( {{x}^{2}}+1 \right)$ có đạo hàm là
A. ${f}'\left( x \right)=-2\text{x}\sin 2\left( {{x}^{2}}+1 \right)$
B. ${f}'\left( x \right)=2\cos \left( {{x}^{2}}+1 \right)$
C. ${f}'\left( x \right)=2x\sin 2\left( {{x}^{2}}+1 \right)$
D. ${f}'\left( x \right)=-4x\sin 2\left( {{x}^{2}}+1 \right)$
A. ${f}'\left( x \right)=-2\text{x}\sin 2\left( {{x}^{2}}+1 \right)$
B. ${f}'\left( x \right)=2\cos \left( {{x}^{2}}+1 \right)$
C. ${f}'\left( x \right)=2x\sin 2\left( {{x}^{2}}+1 \right)$
D. ${f}'\left( x \right)=-4x\sin 2\left( {{x}^{2}}+1 \right)$
${f}'\left( x \right)=2\cos \left( {{x}^{2}}+1 \right){{\left( \cos \left( {{x}^{2}}+1 \right) \right)}^{\prime }}=2\cos \left( {{x}^{2}}+1 \right)\left( -2x \right)\sin \left( {{x}^{2}}+1 \right)=-2x\sin 2\left( {{x}^{2}}+1 \right)$.
Đáp án D.