If for x (0,1/4), the derivatives of tan ⁻¹((6x x)/(1 - 9x³)) is x.g(x), then g(x) equals

Limit, Continuity and Differentiability: JEE Main 2017 Mathematics question

JEE Main 2017 · Session, Shift 1 · Q3676

JEE Main 2017Session, Shift 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

If for

x \in \left( {0,{1 \over 4}} \right)

, the derivatives of

{\tan ^{ - 1}}\left( {{{6x\sqrt x } \over {1 - 9{x^3}}}} \right)

\sqrt x .g\left( x \right)

, then

g\left( x \right)

equals

JEE Main 2017 · Session, Shift 1 · Q3676

JEE Main 2017Session, Shift 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

If for

x \in \left( {0,{1 \over 4}} \right)

, the derivatives of

{\tan ^{ - 1}}\left( {{{6x\sqrt x } \over {1 - 9{x^3}}}} \right)

\sqrt x .g\left( x \right)

, then

g\left( x \right)

equals