Derivative of f(x)=6x+1/3x+10

1. Differentiate $\left(\frac{x}{3} + 6 x\right) + 10$ term by term:

   1. Differentiate $\frac{x}{3} + 6 x$ 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: $6$

      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: $\frac{1}{3}$

      The result is: $\frac{19}{3}$

   2. The derivative of the constant $10$ is zero.

   The result is: $\frac{19}{3}$

The answer is:

$$\frac{19}{3}$$