What is the derivative of ${tan}^{- 1} (3 x^{2})$ $tan^ -1(3x^2)$ ?

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What is the derivative of ${tan}^{- 1} (3 x^{2})$ $tan^ -1(3x^2)$ ?

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Answer 1 · 2016-01-28T05:38:52

$\frac{6 x}{1 - 9 x^{4}}$ $(6x)/(1-9x^4)$

Explanation:

using the chain rule,
$\frac{d}{d x} ({tan}^{- 1} (3 x^{2}))$ $d/(dx)(tan^(-1)(3x^2))$
$= \frac{1}{1 - {(3 x^{2})}^{2}} \cdot \frac{d}{d x} (3 x^{2})$ $=1/(1-(3x^2)^2)*d/(dx)(3x^2)$
$= \frac{1}{1 - 9 x^{4}} \cdot 3 \cdot 2 x$ $=1/(1-9x^4)*3*2x$
$= \frac{6 x}{1 - 9 x^{4}}$ $=(6x)/(1-9x^4)$

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What is the derivative of ${tan}^{- 1} (3 x^{2})$ $tan^ -1(3x^2)$ ?

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What is the derivative of ${tan}^{- 1} (3 x^{2})$ $tan^ -1(3x^2)$ ?