Derivative of 13+30x-4x*sqrt(x)

1. Differentiate $- \sqrt{x} 4 x + \left(30 x + 13\right)$ term by term:

   1. Differentiate $30 x + 13$ term by term:

      1. The derivative of the constant $13$ is zero.

      2. 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: $30$

      The result is: $30$

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

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

         1. Apply the product rule:

            $$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$$

            $f{\left(x \right)} = x$; to find $\frac{d}{d x} f{\left(x \right)}$:

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

            $g{\left(x \right)} = \sqrt{x}$; to find $\frac{d}{d x} g{\left(x \right)}$:

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

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

         So, the result is: $6 \sqrt{x}$

      So, the result is: $- 6 \sqrt{x}$

   The result is: $30 - 6 \sqrt{x}$

The answer is:

$$30 - 6 \sqrt{x}$$