Question

Find y"" for y = −4(x² + 8)³.

Answer 1

To find y'' for y = −4(x² + 8)³, differentiate y with respect to x, then differentiate the result again.

Step-by-step explanation:

To find y'' for y = −4(x² + 8)³:

1. First, differentiate y with respect to x.
2. Then, differentiate the result from step 1 again.

Let's go through the steps:

1. Differentiate y = −4(x² + 8)³ with respect to x:
   y' = -4 * 3(x² + 8)² * (2x) = -24x(x² + 8)²
2. Differentiate y' = -24x(x² + 8)² with respect to x again:
   y'' = -24 * (x² + 8)² + (-24x) * 2(x² + 8) = -24(x² + 8)(x² + 16x + 4)

Therefore, y'' for y = −4(x² + 8)³ is -24(x² + 8)(x² + 16x + 4).