Derivative of 2*exp(x-1)

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

   1. Let $u = x - 1$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 1\right)$:

      1. Differentiate $x - 1$ term by term:

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

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

         The result is: $1$

      The result of the chain rule is:

      $$e^{x - 1}$$

   So, the result is: $2 e^{x - 1}$

2. Now simplify:

   $$2 e^{x - 1}$$

The answer is:

$$2 e^{x - 1}$$