Derivative of (e^x)-e^-x-2x

1. Differentiate $- 2 x + e^{x} - e^{- x}$ term by term:

   1. The derivative of $e^{x}$ is itself.

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Let $u = - x$.

      2. The derivative of $e^{u}$ is itself.

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- x\right)$:

         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: $-1$

         The result of the chain rule is:

         $$- e^{- x}$$

      So, the result is: $e^{- x}$

   3. The derivative of a constant times a function is the constant times the derivative of the function.

      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: $2$

      So, the result is: $-2$

   The result is: $e^{x} - 2 + e^{- x}$

2. Now simplify:

   $$2 \cosh{\left(x \right)} - 2$$

The answer is:

$$2 \cosh{\left(x \right)} - 2$$