What is the first derivative of x(t) with a missing factor of w?

viciado123 · 2009-12-21T00:23:19+00:00

What is the first derivative of x(t) = Acos(wt) + Bsin(wt) + \frac{F}{2mw}tsin(wt) I find: -Awsin(wt) + Bwcos(wt) + \frac{Ftcos(wt)+Fsin(wt)}{2mw} is correct ?

Thread starter viciado123
Start date Dec 20, 2009
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Derivative

In summary, a first derivative problem involves finding the rate of change of a function at a specific point, and is important in various fields such as physics, engineering, and economics. The first derivative can be found using derivative rules, and the second derivative represents the rate of change of the first derivative, providing information about the concavity or curvature of the function. These problems can also be applied in real-life situations, such as calculating velocity, predicting trends, and solving optimization problems.

Dec 20, 2009

viciado123

What is the first derivative of

[tex]x(t) = Acos(wt) + Bsin(wt) + \frac{F}{2mw}tsin(wt)[/tex]

I find:

[tex]-Awsin(wt) + Bwcos(wt) + \frac{Ftcos(wt)+Fsin(wt)}{2mw}[/tex]

is correct ?

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Dec 20, 2009

rochfor1

I believe you're missing a factor of w in the first term of the numerator of the fraction.

1. What is a first derivative problem?

A first derivative problem is a type of mathematical problem that involves finding the rate of change of a function at a specific point. It is also known as finding the slope or gradient of a function at a given point.

2. Why do we need to solve first derivative problems?

Solving first derivative problems is important in a variety of fields, including physics, engineering, economics, and more. It allows us to analyze the behavior of a function and make predictions about its future values.

3. How do you find the first derivative of a function?

The first derivative of a function can be found using the derivative rules, such as the power rule, product rule, quotient rule, and chain rule. These rules can be applied to different types of functions, such as polynomial, exponential, logarithmic, and trigonometric functions.

4. What is the difference between the first derivative and the second derivative?

The first derivative represents the rate of change of a function, while the second derivative represents the rate of change of the first derivative. In other words, the second derivative shows how the slope of a function is changing, which can provide information about the concavity or curvature of the function.

5. How can first derivative problems be applied in real life?

First derivative problems can be applied in various real-life situations, such as calculating the velocity of an object, determining the rate of change of a population, predicting stock market trends, and more. They are also used in optimization problems, where the goal is to find the maximum or minimum value of a function.