Find the derivative of f(x) = (x^2 + 1)(3x - 4).

Step 1: Identify the appropriate differentiation rule.

The function is the product of two functions:
f(x) = (x^2 + 1)(3x - 4)

Use the product rule:
(uv)' = u'v + uv'

Step 2: Define u and v.

Let:
u = x^2 + 1
v = 3x - 4

Then:
u' = 2x
v' = 3

Step 3: Apply the product rule.

f'(x) = (2x)(3x - 4) + (x^2 + 1)(3)

Step 4: Expand each part.

(2x)(3x - 4) = 6x^2 - 8x

3(x^2 + 1) = 3x^2 + 3

Step 5: Combine like terms.

f'(x) = 6x^2 - 8x + 3x^2 + 3

f'(x) = 9x^2 - 8x + 3

Therefore, the derivative is 9x^2 - 8x + 3.