frac{d}{dx} tan^{-1} left( frac{4sqrt{x}}{1 - | vedclass

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(B) Let $y = 	an^{-1} \left( \frac{4\sqrt{x}}{1 - 4x} ight)$.We can rewrite the expression as $y = 	an^{-1} \left( \frac{2(2\sqrt{x})}{1 - (2\sqrt

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$\frac{2}{\sqrt{x}(1 + 4x)}$

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(B) Let $y = 	an^{-1} \left( \frac{4\sqrt{x}}{1 - 4x} ight)$.We can rewrite the expression as $y = 	an^{-1} \left( \frac{2(2\sqrt{x})}{1 - (2\sqrt{x})^2} ight)$.Using the formula $2	an^{-1}(	heta) = 	an^{-1} \left( \frac{2	heta}{1 - 	heta^2} ight)$,let $	heta = 2\sqrt{x}$.Then $y = 2	an^{-1}(2\sqrt{x})$.Differentiating with respect to $x$:$\frac{dy}{dx} = 2 \cdot \frac{1}{1 + (2\sqrt{x})^2} \cdot \frac{d}{dx}(2\sqrt{x})$$\frac{dy}{dx} = 2 \cdot \frac{1}{1 + 4x} \cdot 2 \cdot \frac{1}{2\sqrt{x}}$$\frac{dy}{dx} = \frac{2}{\sqrt{x}(1 + 4x)}$.

$\frac{d}{dx} \tan^{-1} \left( \frac{4\sqrt{x}}{1 - 4x} \right) = $

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