(A) We know that the trigonometric identity for $\sin 2x$ is given by: $\sin 2x = \frac{2 \tan x}{1 + \tan^2 x}$ Substituting this into the expression

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(A) We know that the trigonometric identity for $\sin 2x$ is given by: $\sin 2x = \frac{2 \tan x}{1 + \tan^2 x}$ Substituting this into the expression,we get: $\frac{d}{dx} (\sin 2x)$ Using the chain rule for differentiation,the derivative of $\sin(ax)$ is $a \cos(ax)$: $\frac{d}{dx} (\sin 2x) = 2 \cos 2x$ Therefore,the correct option is $A$.

Class 12 Mathematics Continuity and Differentiation Derivative at a point, Standard differentiation

Easy

$\frac{d}{dx} \left( \frac{2 \tan x}{1 + \tan^2 x} \right) = $ . . . . . .

GSEB 2021 All GSEB

A
$2 \cos 2x$
B
$\sin 2x$
C
$\cos 2x$
D
$2 \sin 2x$

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Continuity and Differentiation

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Derivative at a point, Standard differentiation

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$\frac{d}{dx} \left( \frac{2 \tan x}{1 + \tan^2 x} \right) = $ . . . . . .

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