Find the derivative of y = ( 1/3X + 6)²

Correct Answer is : 232/332 ( 131/331X + 6)

Correct Answer is : 232/332 ( 131/331X + 6)

Test Index

JAMB Mathematics 2016 Paper

Question : 3

Total: 50

\frac{1}{3}

^{2}

Solution:

Concept:

This question tests the chain rule for differentiating a composite power function.

Explanation:

Let

y = \left(\frac{1}{3}x + 6\right)^{2}

Use the chain rule:

\frac{dy}{dx} = 2\left(\frac{1}{3}x + 6\right) \cdot \frac{d}{dx}\left(\frac{1}{3}x + 6\right)

The derivative of the inside term is

\frac{1}{3}

So,

\frac{dy}{dx} = 2\left(\frac{1}{3}x + 6\right) \times \frac{1}{3}

Simplify:

\frac{dy}{dx} = \frac{2}{3}\left(\frac{1}{3}x + 6\right)

Answer:

\frac{2}{3}\left(\frac{1}{3}x + 6\right)

(Option B).

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