First and second derivative assistance please?

In summary, the student is looking for help with derivatives and is having difficulty because he doesn't remember the basic rules.
  • #1
Khamul
24
0

Homework Statement


r = 2/(2 - cos ([tex]\pi[/tex]*t))


Homework Equations



N/A

The Attempt at a Solution


Hello everyone, first I would just like to say (which is obvious since I'm asking :tongue: ) That it's been a long long time since I've had to do derivatives, hence my total cluelessness with this. I've had to integrate frequently in my engineering courses, but this is a problem that arose in my dynamics class...and embarrassingly enough, I'm not even sure where to begin. :confused:

Could someone help me out? I'm going to be unable to proceed with my problem (it involves radius of curvatures) until I get the first and second derivatives of this bad boy. Thanks in advance!
 
Last edited:
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  • #2
Khamul said:

Homework Statement


r = 2/(2 - cos ([tex]\pi[/tex]*t))


Homework Equations



N/A

The Attempt at a Solution


Hello everyone, first I would just like to say (which is obvious since I'm asking :tongue: ) That it's been a long long time since I've had to do derivatives, hence my total cluelessness with this. I've had to integrate frequently in my engineering courses, but this is a problem that arose in my dynamics class...and embarrassingly enough, I'm not even sure where to begin. :confused:

Could someone help me out? I'm going to be unable to proceed with my problem (it involves radius of curvatures) until I get the first and second derivatives of this bad boy. Thanks in advance!

Here's the wikipedia page that will help you out:

http://en.wikipedia.org/wiki/Quotient_rule

I just remember it as "The bottom multiplied by the derivative of the top, minus the top multiplied by the derivative of the bottom, all over the bottom squared."
 
  • #3
Aha! THAT'S the bugger I forgot. I kept thinking of the product rule, and how utterly insane it made this. This helps a bunch, thank you :)
 

1. What is the purpose of finding first and second derivatives?

The first and second derivative of a function provide important information about the behavior and properties of the function. The first derivative represents the rate of change of the function at a specific point, while the second derivative represents the rate of change of the first derivative. These values can help determine the maximum and minimum values of the function, as well as its concavity and inflection points.

2. How do I find the first derivative of a function?

To find the first derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule, depending on the form of the function. These rules involve differentiating each term in the function with respect to the independent variable and simplifying the resulting expression. You can also use online calculators or software to find the derivative.

3. What is the difference between first and second derivatives?

The first derivative measures the rate of change of a function at a specific point, while the second derivative measures the rate of change of the first derivative. In other words, the first derivative tells us how fast the function is changing, while the second derivative tells us how fast the rate of change is changing. The second derivative is also known as the curvature of the function.

4. How do I interpret the first and second derivatives in relation to a function graph?

The first derivative represents the slope of the tangent line at a specific point on the graph of the function. If the first derivative is positive, the function is increasing at that point, and if it is negative, the function is decreasing. The second derivative represents the concavity of the function at a specific point. If the second derivative is positive, the function is concave up, and if it is negative, the function is concave down.

5. Can I use first and second derivatives to find the maximum and minimum values of a function?

Yes, you can use the first and second derivatives to determine the maximum and minimum values of a function. The first derivative can help identify critical points, which are points where the derivative is equal to zero or does not exist. These points can then be evaluated using the second derivative test to determine if they are maximum or minimum values. However, it is important to note that not all maximum and minimum values can be found using derivatives, and other methods may need to be used.

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