Find the coefficient of the squared term in the simplified form for the second derivative., f" (x) for f (x) = (X^3+2x+3) (3x^3-6x^2-8x+1). use the hyphen symbol,-, for negative values.

(Fill-in-the-blank)

Use the product rule:

f' (x) = (x³+2x+3) ' (3x³-6x²-8x+1) + (x³+2x+3) (3x³-6x²-8x+1) '

f' (x) = (3x²+2) (3x³-6x²-8x+1) + (x³+2x+3) (6x²-12x-8)

Use the product rule again:

f'' (x) = (6x) (3x³-6x²-8x+1) + (3x²+2) (9x²-12x-8) + (3x²+2) (6x²-12x-8) + (x³+2x+3) (12x-12)

We only care about the coefficient of the x² term so let's extract the operations of terms that give us x²: (6x) (-8x) + (3x²) (-8) + 2 (9x²) + (3x²) (-8) + 2 (6x²) + (2x) (12x) = - 48x² + (-24x²) + 18x² + (-24x²) + 12x²+24x² = 54x²