Understanding Third Derivatives and Matrix Multiplication in Calculus

  • Thread starter bobsmith76
  • Start date
  • Tags
    Matrix
In summary, the problem involves taking the third derivative and multiplying a 3 by 3 matrix. The person is confused about the progression from the first to the second to the third derivative in the given questions. They also point out a typo in the solution and provide the correct derivatives using the product rule. The person then expresses their understanding and gratitude for the help provided.
  • #1
bobsmith76
336
0

Homework Statement





In the following problem they are taking the third derivative, then multiplying a 3 by 3 matrix. I don't understand how they progress from the first to the second to the third deriviative in the following two questions.

These are the parts of the solution that I really don't understand

Screenshot2012-02-26at101710PMcopy2.png


What's going on? -3 sin t is not the derivative of -3 sin t


Screenshot2012-02-26at101727PMcopy.png


The derivative of e^t(cos t - sin t) is (e^t)(-sin t - cos t) not 2e^t sin t
The derivative of e^t(sin t + cos t) is (e^t)(cos t - sin t) not (2e^t)(cos t)

I don't understand.
 
Last edited:
Physics news on Phys.org
  • #2


I looked at some more examples and they take the derivative for all the others and I understand them. I don't however understand the derivatives of the two above.
 
  • #3


bobsmith76 said:

Homework Statement





In the following problem they are taking the third derivative, then multiplying a 3 by 3 matrix. I don't understand how they progress from the first to the second to the third deriviative in the following two questions.

These are the parts of the solution that I really don't understand

Screenshot2012-02-26at101710PMcopy2.png


What's going on? -3 sin t is not the derivative of -3 sin t
Looks like a typo to me. The middle row in the 2nd column should be -3cos(t).
bobsmith76 said:
Screenshot2012-02-26at101727PMcopy.png


The derivative of e^t(cos t - sin t) is (e^t)(-sin t - cos t) not 2e^t sin t
The derivative of e^t(sin t + cos t) is (e^t)(cos t - sin t) not (2e^t)(cos t)
Your work here is incorrect. Both functions are products, so you need to use the product rule when you differentiate.
bobsmith76 said:
I don't understand.
 
  • #4


excellent. i got it now. i really appreciate your help.
 

What is a 3 by 3 matrix?

A 3 by 3 matrix is a mathematical object that contains 3 rows and 3 columns of numbers or variables. It is commonly represented as a square array with 9 entries.

How do you multiply a 3 by 3 matrix?

To multiply a 3 by 3 matrix, you must follow a specific set of rules. First, the number of columns in the first matrix must match the number of rows in the second matrix. Then, you multiply each entry in the first row of the first matrix by the corresponding entry in the first column of the second matrix. Repeat this for each row and column, and then add the products to get the final result.

Why is multiplying a 3 by 3 matrix important?

Multiplying a 3 by 3 matrix is important in various fields such as physics, engineering, and computer graphics. It allows for the manipulation of multiple variables simultaneously, making complex calculations and transformations more efficient.

What is the difference between multiplying a 3 by 3 matrix and a 2 by 2 matrix?

The main difference between multiplying a 3 by 3 matrix and a 2 by 2 matrix is the number of entries and the resulting dimensions. A 3 by 3 matrix will produce a 3 by 3 matrix as the result, while a 2 by 2 matrix will produce a 2 by 2 matrix.

Are there any special properties or rules when multiplying a 3 by 3 matrix?

Yes, there are several special properties and rules when multiplying a 3 by 3 matrix. These include the commutative property (A*B is not always equal to B*A), the associative property ((A*B)*C is not always equal to A*(B*C)), and the distributive property (A*(B+C) is not always equal to A*B + A*C).

Similar threads

  • Calculus and Beyond Homework Help
Replies
15
Views
744
  • Calculus and Beyond Homework Help
Replies
1
Views
663
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
129
  • Calculus and Beyond Homework Help
Replies
7
Views
3K
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
462
  • Calculus and Beyond Homework Help
Replies
1
Views
818
Back
Top