If y = 4x 3 - 2x 2 + x, find δ y/δ x

Correct Answer is : 12x2 - 4x + 1

Correct Answer is : 12x2 - 4x + 1

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JAMB Mathematics 2014 Paper

Question : 29

Total: 47

\frac{\delta y}{\delta x}

Solution:

Concept:

Differentiate each term of a polynomial term-by-term using the power rule:

\frac{d}{dx}(ax^n) = anx^{n-1}

Explanation:

Given

y = 4x^3 - 2x^2 + x

, find

\frac{\delta y}{\delta x}

Apply the power rule to each term separately.

Derivative of

4x^3

3 \times 4x^{3-1} = 12x^2

Derivative of

-2x^2

2 \times (-2)x^{2-1} = -4x

Derivative of

x

1 \cdot x^{1-1} = 1

Add the results together:

\frac{\delta y}{\delta x} = 12x^2 - 4x + 1

This matches option D.

Answer:

Option D:

12x^2 - 4x + 1

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