Differentiate `tan^(-1){(x^(1//3)+a^(1//3))/(1-(a x)^(1//3))}` with respect to `x`

Explanation

$$ \begin{aligned} &\text { Let } y=\tan ^{-1}\left[\frac{x^{\frac{1}{3}}+a^{\frac{1}{3}}}{1-(a x)^{\frac{1}{3}}}\right] \\ &\Rightarrow y=\tan ^{-1}\left(x^{\frac{1}{3}}\right)+\tan ^{-1}\left(a^{\frac{1}{3}}\right)\left[\text { Since }, \tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right)\right] \end{aligned} $$
Differentiate it with respect to `x` using chain rule,
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