Derivative of y=(sqrtx^2-sqrt18x+sqrt100)

1. Differentiate $\left(\left(\sqrt{x}\right)^{2} - \sqrt{18 x}\right) + \sqrt{100}$ term by term:

   1. Differentiate $\left(\sqrt{x}\right)^{2} - \sqrt{18 x}$ term by term:

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

      2. Apply the power rule: $u^{2}$ goes to $2 u$

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

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

         The result of the chain rule is:

         $$1$$

      4. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Let $u = 18 x$.

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

         3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 18 x$:

            1. The derivative of a constant times a function is the constant times the derivative of the function.

               1. Apply the power rule: $x$ goes to $1$

               So, the result is: $18$

            The result of the chain rule is:

            $$\frac{3 \sqrt{2}}{2 \sqrt{x}}$$

         So, the result is: $- \frac{3 \sqrt{2}}{2 \sqrt{x}}$

      The result is: $1 - \frac{3 \sqrt{2}}{2 \sqrt{x}}$

   2. The derivative of the constant $\sqrt{100}$ is zero.

   The result is: $1 - \frac{3 \sqrt{2}}{2 \sqrt{x}}$

The answer is:

$$1 - \frac{3 \sqrt{2}}{2 \sqrt{x}}$$