Find dy/dx. If y = 3x 3 + 2x 2 + 3x + 1

Correct Answer is : 9x2 + 4x + 3

Correct Answer is : 9x2 + 4x + 3

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JAMB Mathematics 2016 Paper

Question : 37

Total: 50

Find

\frac{dy}{dx}

. If y = 3x³ + 2x² + 3x + 1

Solution:

Concept:

Differentiate the polynomial term by term using the power rule.

Explanation:

Given

y = 3x^3 + 2x^2 + 3x + 1

For each term, use the rule

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

Differentiating

3x^3

gives

3 \cdot 3x^{3-1} = 9x^2

Differentiating

2x^2

gives

2 \cdot 2x^{2-1} = 4x

Differentiating

3x

gives

3

Differentiating the constant

1

gives

0

Adding these results,

\frac{dy}{dx} = 9x^2 + 4x + 3

Answer:

9x^2 + 4x + 3

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