Simplifying wrong or completely wrong?

[iRaid]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

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

Answer is:
3sin(6x-4)


What am I missing here ?

 

[Mark44]

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.

 

[lurflurf]

The identity

sin²(u)=(1/2)[1-cos(2x)]
so
[sin²(u)]'=[(1/2)[1-cos(2x)]]'=sin(2u)u'

 

[iRaid]

Ah, I remember that now, now I'll remember that identity, thank you.