The differential coefficient of ${tan}^{- 1} m x$ with respect to $x$ is

\frac{x}{m \sqrt{1 + x^{2}}}

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\frac{m}{1 + m^{2} x^{2}}

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\frac{m^{2} x}{1 + x^{2}}

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\frac{m^{2} x}{1 - m x^{2}}

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Solution

The correct option is B $\frac{m}{1 + m^{2} x^{2}}$
On differentiating, we get

$\frac{d}{d x} ({tan}^{- 1} m x)$

$= \frac{m}{1 + {(m x)}^{2}}$

$= \frac{m}{1 + m^{2} x^{2}}$

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