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Simplifying wrong or completely wrong?

  • Thread starter iRaid
  • Start date
  • #1
559
8

Homework Statement


Find dy/dx.
[itex]y=sin^{2}(3x-2)[/itex]


Homework Equations





The Attempt at a Solution


Using the chain rule,
[itex]y=sin^{2}u[/itex]
[itex]y'=2sinucosu[/itex]
[itex]u=3x-2[/itex]
[itex]u'=3[/itex]

[itex]\frac{dy}{dx}=6sin(3x-2)cos(3x-2)[/itex]

Answer is:
[itex]3sin(6x-4)[/itex]


What am I missing here ?
 

Answers and Replies

  • #2
33,314
5,006
Your answer is correct, and so is the other answer you show. They are using the identity sin(2A) = 2sin(A)cos(A). In your problem A = 3x - 2.
 
  • #3
lurflurf
Homework Helper
2,428
127
The identity

sin2(u)=(1/2)[1-cos(2x)]
so
[sin2(u)]'=[(1/2)[1-cos(2x)]]'=sin(2u)u'
 
  • #4
559
8
Ah, I remember that now, now I'll remember that identity, thank you.
 

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