Tính vi phân của hàm số $y=\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}$

$\begin{array}{l}y\text{'}=\frac{1}{2\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}}.\left[\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}\right]\text{'}\\ =\frac{1}{2\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}}.\text{\hspace{0.17em}[\hspace{0.17em}}-\sin \sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}\text{]}.\left[\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}\right]\text{'}\\ =\frac{-\sin \sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}{2\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}}.\frac{1}{2\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}.\left[x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)\right]\text{'}\\ =\frac{-\sin \sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}{2\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}}.\frac{1}{2\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}.\text{[}1+\text{\hspace{0.17em}}c\text{os(2x+sin x ). (2x+sin x )'] }\\ =\frac{-\sin \sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}{2\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}}.\frac{1}{2\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}.\text{[}1+\text{\hspace{0.17em}}c\text{os(2x+sin x).(2 +}c\text{osx)]}\\ =\frac{-\sin \sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}{2\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}}.\frac{1+\text{\hspace{0.17em}}c\text{os(2x+sin x).(2 +}c\text{osx)}}{2\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}\end{array}$

Vi phân của hàm số là

$dy=\frac{-\sin \sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}{2\sqrt{\text{cos}\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}}.\frac{1+\text{\hspace{0.17em}}c\text{os(2x+sin x).(2 +}c\text{osx)}}{2\sqrt{x\text{}+\text{}\sin \left(2x+\text{}\sin x\right)}}dx$

Chọn D