Derivative of 1/(y*y)

1. Let $u = y y$.

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

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

   1. Apply the product rule:

      $$\frac{d}{d y} f{\left(y \right)} g{\left(y \right)} = f{\left(y \right)} \frac{d}{d y} g{\left(y \right)} + g{\left(y \right)} \frac{d}{d y} f{\left(y \right)}$$

      $f{\left(y \right)} = y$; to find $\frac{d}{d y} f{\left(y \right)}$:

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

      $g{\left(y \right)} = y$; to find $\frac{d}{d y} g{\left(y \right)}$:

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

      The result is: $2 y$

   The result of the chain rule is:

   $$- \frac{2}{y^{3}}$$

The answer is:

$$- \frac{2}{y^{3}}$$