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Find $\Large\frac{dy}{dx}$when$y=\tan^{-1}\bigg[\Large\frac{x^{\frac{1}{3}}+a^{\frac{1}{3}}}{1-x^{\frac{1}{3}}a^{\frac{1}{3}}}\bigg]$

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  • $ tan^{-1}\large\frac{x+y}{1-xy} = tan^{-1}x+tan^{-1}y$
$ y=tan^{-1}\: x^{\large\frac{1}{3}}+tan^{-1}\: a^{\large\frac{1}{3}}$
$ \large\frac{dy}{dx}=\large\frac{1}{1+x^{\large\frac{2}{3}}}$x$\large \frac{1}{3x^{\large\frac{2}{3}}}$

 

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