Taking the derivative (no numbers)

In summary, the conversation discusses a differential characteristic equation involving cosine and sine, with the individual providing their solution and asking for confirmation. They also mention simplifying the equation, but it is not shown in the image provided.
  • #1
ME_student
108
5

Homework Statement


So I'd rather not type out the whole equation I am differentiating with respect to t... Sorry admins. My written work is on the image. I just want to make sure my work is correct.

Homework Equations


The equation is a differential characteristic equation with cos and sin.

The Attempt at a Solution


The attempt solution is on the image. Start at Line 1 to Line 2.

I applied product rule twice with chain rule. We are taking the derivative of the formula with respect to t.
 

Attachments

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  • #2
From what I can see in that little thumbnail, it looks fine.
 
  • #3
vela said:
From what I can see in that little thumbnail, it looks fine.[/QUOTE

Okay thanks. Does my simplifying look fine as well?
 
  • #4
You simplified? It's hard to see anything in that little thumbnail, so I'll take your word for it. I suppose I could click on the thumbnail to bring up the larger image, but I'd rather not.
 
  • #5
ME_student said:
Okay thanks. Does my simplifying look fine as well?
No .

sin(θ) + cos(θ) ≠ 1

However, sin2(θ) + cos2(θ) = 1, but you don't have that anywhere.
 
  • #6
Sorry for the small iMage. I got it figured out.
 

Attachments

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Related to Taking the derivative (no numbers)

1. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is the slope of the tangent line at that point and can also be described as the instantaneous rate of change.

2. Why is taking the derivative important?

Taking the derivative is important because it allows us to analyze the behavior of a function and understand how it changes over time. It is also used in many real-world applications, such as physics, engineering, and economics, to model and predict the behavior of systems.

3. What is the process of taking a derivative?

The process of taking a derivative involves using mathematical rules and formulas to find the derivative of a function. These rules include the power rule, product rule, quotient rule, and chain rule. It is important to practice and understand these rules in order to accurately take derivatives.

4. How do I know when to use the different derivative rules?

The different derivative rules are used depending on the type of function you are trying to find the derivative of. For example, the power rule is used for functions with only variables raised to a power, while the product rule is used for functions that are multiplied together. It is important to recognize the type of function and apply the appropriate rule.

5. Can I take the derivative of any function?

In most cases, yes, you can take the derivative of any function. However, there are some functions that are not differentiable, such as those with sharp corners or discontinuities. It is important to understand the properties of a function before attempting to take its derivative.

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