Derivative of 225/x+x+6

1. Differentiate $\left(x + \frac{225}{x}\right) + 6$ term by term:

   1. Differentiate $x + \frac{225}{x}$ 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: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$

         So, the result is: $- \frac{225}{x^{2}}$

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

      The result is: $1 - \frac{225}{x^{2}}$

   2. The derivative of the constant $6$ is zero.

   The result is: $1 - \frac{225}{x^{2}}$

The answer is:

$$1 - \frac{225}{x^{2}}$$