Derivative of y*(y-2)

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 $1$

   $g{\left(y \right)} = y - 2$; to find $\frac{d}{d y} g{\left(y \right)}$:

   1. Differentiate $y - 2$ term by term:

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

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

      The result is: $1$

   The result is: $2 y - 2$

The answer is:

$$2 y - 2$$