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MATHEMATICS

JAMB 2016 - Question 34

Mathematics 2016 JAMB Past Questions - Question 34: If y=2x3+6x2+6x+1,Find dy/dx

If y=2x3+6x2+6x+1,Find dy/dx

A: 6x²+12x+1

B: 6x²+6x+1

C: 6x²+6x+6

D: 6x²+12x+6

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Correct Answer

Explanation

To find \(\frac{dy}{dx}\) for the function \(y = 2x^3 + 6x^2 + 6x + 1\), we need to differentiate each term of the function with respect to x.The derivative of \(2x^3\) with respect to x is \(6x^2\), the derivative of \(6x^2\) with respect to x is \(12x\), the derivative of \(6x\) with respect to x is \(6\), and the derivative of the constant term \(1\) is \(0\).Therefore, \(\frac{dy}{dx} = 6x^2 + 12x + 6\).