Question

What is the derivative of sin2(x)?

Answer 1

Answer:

sin(2x)

Step-by-step explanation:

Use the chain rule:

$\displaystyle\frac{d}{dx}(\sin^2x)\\\\=\frac{d}{d(\sin x)}(\sin^2 x)\times\frac{d(\sin x)}{dx}\\\\= (2\sin x) \times\cos x\\\\= 2\,\sin x\,\cos x\\\\= \sin 2x$

Answer 2

Answer:

2 cos 2x

Step-by-step explanation:

By CHAIN RULE,

f ' ( g ( x ) ) ⋅ g ' ( x )  

We essentially have a composite function   , f ( g ( x ) )

where ,

f ( x ) = sin x ⇒ f ' ( x ) = cos x

and  

g ( x ) = 2 x ⇒ g ' ( x ) = 2  

Then we get,

cos ( 2 x ) ⋅ 2  ⇒ 2 cos 2 x

Hence,d/dx of sin(2x)=2cos(2x)