Derivative of y=sinsqrt1+sqrtx

1. Differentiate $\sqrt{x} + \sin{\left(\sqrt{1} \right)}$ term by term:

   1. Let $u = \sqrt{1}$.

   2. The derivative of sine is cosine:

      $$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$$

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{1}$:

      1. The derivative of the constant $\sqrt{1}$ is zero.

      The result of the chain rule is:

      $$0$$

   4. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$

   The result is: $\frac{1}{2 \sqrt{x}}$

The answer is:

$$\frac{1}{2 \sqrt{x}}$$