Derivative of y=√x+3√x+4√x

1. Differentiate $4 \sqrt{x} + \left(\sqrt{x} + 3 \sqrt{x}\right)$ term by term:

   1. Differentiate $\sqrt{x} + 3 \sqrt{x}$ term by term:

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

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

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

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

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

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

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

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

   The result is: $\frac{4}{\sqrt{x}}$

The answer is:

$$\frac{4}{\sqrt{x}}$$