Section 2.4: Reading questions on the product rule

Read Example 51 on pages 86-87 in the APEX Calculus textbook (version 3). Using Example 51 as a guide, answer the following questions. Suppose $y = (x^3+7x) (4x^2+9)$. Here are two different ways to compute the derivative of this function.

1. First, expand the given product and then compute the derivative.
   $y =$
   $y^{\,\prime} =$
2. First, apply the product rule and then simplify the result.
   $y^{\,\prime} = f' g + f g' = \Big($ $\Big) \cdot \Big($ $\Big) + \Big($ $\Big) \cdot \Big($ $\Big)$
   $y^{\,\prime} =$ (simplified)