(frac{d}{dx} [log (4x^3 – 2x)]) is equal to
-
A.
(frac{12x – 2}{4x^2}) -
B.
(frac{43x^2 – 2x}{7x}) -
C.
(frac{4x^2 – 2}{7x + 6}) -
D.
(frac{12x^2 – 2}{4x^3 – 2x})
Correct Answer: Option D
Explanation
(frac{d}{dx} [log (4x^3 – 2x)]) … (1)
Let u = 4x(^3) – 2x.
(frac{mathrm d}{mathrm d x} (log (4x^3 – 2x)) = (frac{mathrm d}{mathrm d u})(frac{mathrm d u}{mathrm d x}))
(frac{mathrm d}{mathrm d u} (log u)) = (frac{1}{u})
(frac{mathrm d u}{mathrm d x} = 12x^2 – 2)
(therefore frac{d}{dx} [log (4x^3 – 2x)] = frac{12x^2 – 2}{u})
= (frac{12x^2 – 2}{4x^3 – 2x})
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