If y = tan - 1 ( 3 x - x 3 1 - 3 x 2 ) , - 1 3 x 1 3 , then d y d x is:

Question

If $y = \tan^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}})$ , $- \frac{1}{\sqrt{3}} < x < \frac{1}{\sqrt{3}}$ , then $\frac{d y}{d x}$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{3}{1 + x^{2}}$

Explanation:

$y = \tan^{- 1} (\frac{3 x - x^{3}}{1 - 3 x^{2}}) = 3 \tan^{- 1} x$

$\frac{d y}{d x} = \frac{3}{1 + x^{2}}$

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