To find the derivative of the function f(x) = (2x + 3)(3x² + x), we can use the product rule.

The product rule states that if we have two functions, u(x) and v(x), their derivative can be calculated as follows:

(uv)' = u'v + uv'

Let's apply the product rule to the given function:

f(x) = (2x + 3)(3x² + x)

Using the product rule, we have:

f'(x) = (2x + 3)'(3x² + x) + (2x + 3)(3x² + x)'

Now, let's find the derivatives of each term:

(2x + 3)' = 2

(3x² + x)' = 6x + 1

Substituting these derivatives back into the equation, we have:

f'(x) = 2(3x² + x) + (2x + 3)(6x + 1)

Simplifying further, we get:

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

Combining like terms, we have:

f'(x) = 18x² + 10x + 18x + 3

Finally, simplifying the equation, we obtain the derivative of f(x):

f'(x) = 18x² + 28x + 3