Derivative of 1-1/(y/(-3))^2

1. Differentiate $1 - \frac{1}{\left(\frac{y}{-3}\right)^{2}}$ 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 $u = \left(\frac{y}{-3}\right)^{2}$.

      2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$

      3. Then, apply the chain rule. Multiply by $\frac{d}{d y} \left(\frac{y}{-3}\right)^{2}$:

         1. Let $u = \frac{y}{-3}$.

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

         3. Then, apply the chain rule. Multiply by $\frac{d}{d y} \frac{y}{-3}$:

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

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

               So, the result is: $\frac{1}{-3}$

            The result of the chain rule is:

            $$\frac{2 y}{9}$$

         The result of the chain rule is:

         $$- \frac{18}{y^{3}}$$

      So, the result is: $\frac{18}{y^{3}}$

   The result is: $\frac{18}{y^{3}}$

The answer is:

$$\frac{18}{y^{3}}$$