Simplifying wrong or completely wrong?

In summary, simplifying wrong or completely wrong can aid in identifying errors or misconceptions, leading to a better understanding of the topic. To identify if something is wrong or completely wrong, one can review the information, compare it to reliable sources, and critically analyze the logic behind it. However, simplifying wrong or completely wrong can be harmful if it leads to a false understanding of a topic. It is important to verify information and seek feedback before simplifying it. Whether it is acceptable to simplify information depends on the context, but it should not alter the accuracy of the information. To avoid simplifying wrong or completely wrong, it is crucial to critically evaluate information and seek feedback from experts or reliable sources.
  • #1
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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 ?
 
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  • #2
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
The identity

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

1. What is the importance of simplifying wrong or completely wrong?

Simplifying wrong or completely wrong can help identify errors or misconceptions and lead to a better understanding of the topic. It can also help in finding the correct solution or approach to a problem.

2. How do you identify if something is wrong or completely wrong?

This can be done by carefully reviewing the information or data, comparing it to reliable sources, and critically analyzing the logic and reasoning behind it. It is also helpful to consult with experts or seek feedback from peers.

3. Can simplifying wrong or completely wrong be harmful?

In some cases, simplifying wrong or completely wrong can lead to a false understanding of a topic and hinder learning. It is important to double-check and verify information before simplifying it.

4. Is it okay to simplify information even if it is not completely wrong?

It depends on the context. Simplifying information can be helpful in making it more accessible and understandable, but it should not alter the accuracy or validity of the information.

5. How can we avoid simplifying wrong or completely wrong?

To avoid simplifying wrong or completely wrong, it is important to critically evaluate information and carefully consider the source. It is also helpful to seek feedback and clarification from experts or reliable sources.

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