Derivative of (1/4x+1)+3x

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

   1. Differentiate $\frac{x}{4} + 1$ term by term:

      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: $\frac{1}{4}$

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

      The result is: $\frac{1}{4}$

   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: $3$

   The result is: $\frac{13}{4}$

The answer is:

$$\frac{13}{4}$$