Derivative of (1/x)+(4x)-7

1. Differentiate $\left(4 x + \frac{1}{x}\right) - 7$ term by term:

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

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

      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: $4$

      The result is: $4 - \frac{1}{x^{2}}$

   2. The derivative of the constant $-7$ is zero.

   The result is: $4 - \frac{1}{x^{2}}$

The answer is:

$$4 - \frac{1}{x^{2}}$$