Given,

f(x) = (2x² + 1)(3x + 2)

⇒ f(x) = 6x³ + 4x² + 3x + 2

we need to find f’(x), so differentiating both sides with respect to x –

∴

Using algebra of derivatives –

⇒ f’(x) =

Use the formula:

∴ f’(x) = 6(3x^{3 – 1}) + 4(2x^{2 – 1}) + 3(x^{1 – 1}) + 0

⇒ f’(x) = 18x² + 8x + 3 + 0

∴ f’(x) = 18x² + 8x + 3