Answer
384.6k+ views
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 $x$ .
Additional Information:
Differentiation is the essence of Calculus. A derivative is defined because the instantaneous rate of change in function supported one in every of its variables. it's just like finding the slope of a tangent to the function at some extent. we've got following rules in differentiation ,
• Sum and Difference rule that claims (u(x) ± v(x))’=u'(x)±v'(x)
• Product rule that says (u(x) × v(x))’=u′(x)×v(x)+u(x)×v′(x)
• Quotient Rule that claims (u(x)/v(x))’ =(u′(x)×v(x)−u(x)×v′(x))/(v(x))2
• Chain Rule that says dy(u(x))/dx = dy/du × du/dx
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
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 $x$ .
Additional Information:
Differentiation is the essence of Calculus. A derivative is defined because the instantaneous rate of change in function supported one in every of its variables. it's just like finding the slope of a tangent to the function at some extent. we've got following rules in differentiation ,
• Sum and Difference rule that claims (u(x) ± v(x))’=u'(x)±v'(x)
• Product rule that says (u(x) × v(x))’=u′(x)×v(x)+u(x)×v′(x)
• Quotient Rule that claims (u(x)/v(x))’ =(u′(x)×v(x)−u(x)×v′(x))/(v(x))2
• Chain Rule that says dy(u(x))/dx = dy/du × du/dx
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
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)