Derivative of y=(x²-1)(x²-4)(x²-9)

1. Apply the product rule:

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

   $f{\left(x \right)} = \left(x^{2} - 4\right) \left(x^{2} - 1\right)$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Apply the product rule:

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

      $f{\left(x \right)} = x^{2} - 1$; to find $\frac{d}{d x} f{\left(x \right)}$:

      1. Differentiate $x^{2} - 1$ term by term:

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

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

         The result is: $2 x$

      $g{\left(x \right)} = x^{2} - 4$; to find $\frac{d}{d x} g{\left(x \right)}$:

      1. Differentiate $x^{2} - 4$ term by term:

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

         2. The derivative of the constant $-4$ is zero.

         The result is: $2 x$

      The result is: $2 x \left(x^{2} - 4\right) + 2 x \left(x^{2} - 1\right)$

   $g{\left(x \right)} = x^{2} - 9$; to find $\frac{d}{d x} g{\left(x \right)}$:

   1. Differentiate $x^{2} - 9$ term by term:

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

      2. The derivative of the constant $-9$ is zero.

      The result is: $2 x$

   The result is: $2 x \left(x^{2} - 4\right) \left(x^{2} - 1\right) + \left(x^{2} - 9\right) \left(2 x \left(x^{2} - 4\right) + 2 x \left(x^{2} - 1\right)\right)$

2. Now simplify:

   $$6 x^{5} - 56 x^{3} + 98 x$$

The answer is:

$$6 x^{5} - 56 x^{3} + 98 x$$