Find the derivative the following ways:
Using the Product Rule or the Quotient Rule. Simplify your result.
f(x) = (x - 1)(3x + 4)

Verified step by step guidance

1. Step 1: Identify the functions to apply the Product Rule. Here, we have two functions: \( u(x) = x - 1 \) and \( v(x) = 3x + 4 \).
2. Step 2: Recall the Product Rule formula: \( (uv)' = u'v + uv' \). This means we need to find the derivatives of \( u(x) \) and \( v(x) \).
3. Step 3: Differentiate \( u(x) = x - 1 \). The derivative \( u'(x) \) is 1, since the derivative of \( x \) is 1 and the derivative of a constant is 0.
4. Step 4: Differentiate \( v(x) = 3x + 4 \). The derivative \( v'(x) \) is 3, since the derivative of \( 3x \) is 3 and the derivative of a constant is 0.
5. Step 5: Apply the Product Rule: \( f'(x) = u'v + uv' = (1)(3x + 4) + (x - 1)(3) \). Simplify the expression to find the derivative.