Mathematics 2001 JAMB Past Questions - Question 33: differentiate (2x +5)² (x-4) with respect to x

Correct Answer

A

Explanation

To differentiate the expression (2x + 5)² (x - 4) with respect to x, we can use the product rule and the chain rule.Let's denote the expression as f(x) = (2x + 5)² (x - 4).Using the product rule, the derivative of f(x) is given by:f'(x) = (2x + 5)² * (x - 4)' + (x - 4) * (2x + 5)²'To find the derivative of (2x + 5)², we can apply the chain rule. The derivative of (2x + 5)² with respect to (2x + 5) is 2(2x + 5).Similarly, the derivative of (x - 4) with respect to x is 1.Now, let's substitute these derivatives into the equation:f'(x) = (2x + 5)² * 1 + (x - 4) * 2(2x + 5)Simplifying further:f'(x) = (2x + 5)² + 2(x - 4)(2x + 5)Expanding and combining like terms:f'(x) = (4x² + 20x + 25) + (4x² + 10x - 40)f'(x) = 8x² + 30x - 15Therefore, the derivative of (2x + 5)² (x - 4) with respect to x is 8x² + 30x - 15.