If for \( x \in\left(0, \frac{1}{4}\right) \), the derivative of \( \tan ^{-1}\left(\frac{6 x \s...
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If for \( x \in\left(0, \frac{1}{4}\right) \), the derivative of \( \tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^{3}}\right) \) is
\( \mathrm{P} \) \( \sqrt{x} \cdot g(x) \), then \( g(x) \) equals :
[JEE Main - 2017]
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(1) \( \frac{3}{1+9 x^{3}} \)
(2) \( \frac{9}{1+9 x^{3}} \)
(3) \( \frac{3 x \sqrt{x}}{1-9 x^{3}} \)
(4) \( \frac{3 x}{1-9 x^{3}} \)
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