Derivative of 1-exp^(-0.1*x)

1. Differentiate $1 - e^{- \frac{x}{10}}$ term by term:

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

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

      1. Let $u = - \frac{x}{10}$.

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

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- \frac{x}{10}\right)$:

         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: $- \frac{1}{10}$

         The result of the chain rule is:

         $$- \frac{e^{- \frac{x}{10}}}{10}$$

      So, the result is: $\frac{e^{- \frac{x}{10}}}{10}$

   The result is: $\frac{e^{- \frac{x}{10}}}{10}$

The answer is:

$$\frac{e^{- \frac{x}{10}}}{10}$$