Derivative of ((1)/(x^16))+(2345)

1. Differentiate $2345 + 1 \cdot \frac{1}{x^{16}}$ term by term:

   1. Apply the quotient rule, which is:

      $$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$$

      $f{\left(x \right)} = 1$ and $g{\left(x \right)} = x^{16}$.

      To find $\frac{d}{d x} f{\left(x \right)}$:

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

      To find $\frac{d}{d x} g{\left(x \right)}$:

      1. Apply the power rule: $x^{16}$ goes to $16 x^{15}$

      Now plug in to the quotient rule:

      $- \frac{16}{x^{17}}$

   2. The derivative of the constant $2345$ is zero.

   The result is: $- \frac{16}{x^{17}}$

The answer is:

$$- \frac{16}{x^{17}}$$