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# If $y = \sin (2x)$ , then $\dfrac{{dy}}{{dx}}$ is equal toChoose the correct option from the following options:A. $2\cos (2x)$B. $2\cos (x)$C. $2\sin (x)$D. $2\sin (2x)$

Last updated date: 25th Jul 2024
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Hint:For solving this particular question we must know that Differentiation of trigonometric function sine of variable $x$ is equal to cosine of variable $x$ , and differentiation of $\sin ax = a\cos ax$ where $a$ is any constant and $x$ is the variable .

Complete solution step by step:
It is given it the question that ,
$y = \sin 2x$ (given)
Now , differentiate on both sides with respect to $x$ , we will get ,
$\dfrac{{dy}}{{dx}} = \dfrac{d}{{dx}}(\sin 2x)$
$\Rightarrow \dfrac{{dy}}{{dx}} = \cos (2x).2$ (since differentiation of $\sin ax = a\cos ax$ )
$= 2\cos 2x$
Therefore , $\dfrac{{dy}}{{dx}} = 2\cos 2x$ .
And we can say that option A is the correct option.
Formula used: For solving this particular question we used ,
$\dfrac{d}{{dx}}(\sin ax) = a\cos ax$ ,where $a$is any constant and $x$ is the variable .
Differentiation of trigonometric function sine of variable $x$ is equal to cosine of variable $x$ .

Note: The differentiation of a function $f(x)$ is represented as $f'(x)$ . If $f(x) = y$, then $f'(x) =\dfrac{{dy}}{{dx}}$ , which means $y$ is differentiated with respect to $x$ Differentiation of trigonometric function sine of variable $x$ is equal to cosine of variable $x$ , and differentiation of $\sin ax = a\cos ax$ where $a$ is any constant and $x$ is the variable