d/dx [ (4x³ - 2x)] is equal to

Correct Answer is : 12x2−24x3−2x12x² - 2/4x³ - 2x4x3−2x12x2−2

Correct Answer is : 12x2−24x3−2x12x² - 2/4x³ - 2x4x3−2x12x2−2

Test Index

JAMB Mathematics 2019 Paper

Question : 25

Total: 73

\frac{d}{dx} [\log (4x^3 - 2x)]

is equal to

Solution:

Concept:

Use the chain rule to differentiate a logarithmic expression where the argument is a polynomial.

Explanation:

Let

u = 4x^3 - 2x

Then the given function is

\log u

By the chain rule,

\frac{d}{dx}[\log u] = \frac{d}{du}[\log u] \cdot \frac{du}{dx}

Taking

\log

as the natural logarithm, as implied by the options,

\frac{d}{du}[\log u] = \frac{1}{u}

Now differentiate

u

\frac{du}{dx} = 12x^2 - 2

Substitute back into the chain rule:

\frac{d}{dx}[\log(4x^3 - 2x)] = \frac{1}{4x^3 - 2x} \cdot (12x^2 - 2)

So the derivative is

\frac{12x^2 - 2}{4x^3 - 2x}

This matches option D.

Answer:

\frac{12x^2 - 2}{4x^3 - 2x}

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