Simplifying wrong or completely wrong?

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Homework Help Overview

The problem involves finding the derivative of the function y = sin²(3x - 2) with respect to x, utilizing differentiation techniques such as the chain rule and trigonometric identities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the chain rule for differentiation and expresses confusion regarding the discrepancy between their answer and an alternative form presented. Some participants discuss the use of trigonometric identities to reconcile the different expressions for the derivative.

Discussion Status

Participants have provided insights regarding the correctness of the original poster's approach and the validity of the alternative answer. There is acknowledgment of the trigonometric identity that relates the two forms of the derivative, indicating a productive exploration of the topic.

Contextual Notes

There is mention of the identity sin(2A) = 2sin(A)cos(A) as well as another identity involving sin²(u), which may suggest that participants are navigating through various methods of expressing the derivative.

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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 ?
 
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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.
 
The identity

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

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