Derivative of 1-(2-x/a)^n

1. Differentiate $1 - \left(2 - \frac{x}{a}\right)^{n}$ 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 $u = 2 - \frac{x}{a}$.

      2. Apply the power rule: $u^{n}$ goes to $\frac{n u^{n}}{u}$

      3. Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} \left(2 - \frac{x}{a}\right)$:

         1. Differentiate $2 - \frac{x}{a}$ term by term:

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

            2. 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: $- \frac{1}{a}$

            The result is: $- \frac{1}{a}$

         The result of the chain rule is:

         $$- \frac{n \left(2 - \frac{x}{a}\right)^{n}}{a \left(2 - \frac{x}{a}\right)}$$

      So, the result is: $\frac{n \left(2 - \frac{x}{a}\right)^{n}}{a \left(2 - \frac{x}{a}\right)}$

   The result is: $\frac{n \left(2 - \frac{x}{a}\right)^{n}}{a \left(2 - \frac{x}{a}\right)}$

2. Now simplify:

   $$\frac{n \left(2 - \frac{x}{a}\right)^{n}}{2 a - x}$$

The answer is:

$$\frac{n \left(2 - \frac{x}{a}\right)^{n}}{2 a - x}$$