Final answer:
To calculate the derivative of (2x^2 + 5)(4x - 3), apply the product rule, which results in the derivative being 24x^2 - 12x + 20.
Step-by-step explanation:
To find the derivative of the product of two functions using the product rule, we apply the formula: (fg)' = f'g + fg'. In this case, we are looking at the functions f(x) = 2x2 + 5 and g(x) = 4x - 3. First, we find the derivatives of each function separately. The derivative of f(x) is f'(x) = 4x, and the derivative of g(x) is g'(x) = 4. Now applying the product rule:
Derivative of (2x2 + 5)(4x - 3) = (4x)(4x - 3) + (2x2 + 5)(4)
This simplifies to:
16x2 - 12x + 8x2 + 20
Combining like terms, we get the final result:
24x2 - 12x + 20