Question

Differentiate sin^2(2x+1) with respect to x.

Answer 1

This question is related to chain rule so the differentiation is like
d(sin^2(2x+1))/dx = 2sin(2x+1)*cos(2x+1)*2
= 2sin(4x+2)
this is because 2sinxcosx = sin2x
so your answer is 2sin(4x+2).
In chain rule like in this question first you do the differentiation of power component which is 2sin(2x+1)then we do the differentiation of sin(2x+1) itself which is cos(2x+1) then we do the differentiation of 2x+1 which is 2 only so your result is like 2sin(2x+1)*cos(2x+1)*2.

Answer 2

HEY BUDDY..!!!

HERE'S THE ANSWER..

_____________________________

♠️ We'll be using chain rule in this , and I'll try to make it more clear so u can solve this kind on question.

# CHAIN RULES ( we'll will differentiating in this order

▶️ Power of function => function => angle

✔️ [ sin^2 ( 2 x + 1 ) ] '

=> 2 sin ( 2 x + 1 ) . [ sin ( 2 x + 1 ) ] ' // Power

=> 2 sin ( 2 x + 1 ) . cos ( 2 x + 1 ) . [ ( 2 x + 1 ) ] ' // function

=> 2 sin ( 2 x + 1 ) . cos ( 2 x + 1 ) . 2

▶️ Now to make your answer clear sprate constants

=> [ 4 sin ( 2 x + 1 ) . cos ( 2 x + 1 ) ]

⏺️ As we know

✔️ 2 sin x . cos x = sin 2 x


=> sin 2 ( 2 x + 1 ) . 2

=> [ 2 sin 2 ( 2 x + 1 ) ] ✔️✔️

⏺️ This is our final answer..

HOPE HELPED..

JAI HIND..

:-)