If $y=\sqrt{\cosh x+\sqrt{\cosh x}}$, then $\frac{d y}{d x}=$

• A

  $\frac{\sinh x\left(2 y^2+2 \cosh x+1\right)}{4 y\left(y^2+\cosh x\right)}$
• B

  $\frac{\sinh x\left(2 y^2-2 \cosh x-1\right)}{4 y\left(y^2-\cosh x\right)}$
• C

  $\frac{\sinh x(1-2 \sqrt{\cosh x})}{4 y \sqrt{\cosh x}}$
• Correct answer
  D

  $\frac{\sinh x(1+2 \sqrt{\cosh x})}{4 y \sqrt{\cosh x}}$

Hence, the correct answer is option: 'D'.