What is the solution for the function in the given equation?

Thread starter tombk2
Start date Apr 15, 2009

In summary, the purpose of finding the function (antidiff) is to determine the original function from its derivative. The process involves using integration techniques to reverse the process of differentiation, such as known integration formulas, substitution, or other methods. It is important because it allows us to solve problems involving rates of change and to find the original function from its derivative. Common techniques include the power rule, integration by parts, u-substitution, and trigonometric substitution, but there are limitations as not all functions can be antidifferentiated and some may require more advanced techniques. It is also important to check for a constant of integration when solving an antidifferentiation problem.

Apr 15, 2009

tombk2

Homework Statement

[tex]f:\Re\rightarrow\Re[/tex]
[tex]e^xf(x)+e^xf\prime(x)=f(x)[/tex]
Find f(x)

Homework Equations

The Attempt at a Solution

i don't know if [tex] f(x)\neq 0[/tex] so i can't divide by [tex]f(x)[/tex] which would make things pretty simple.

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Apr 15, 2009

cse63146

Try this:

put all f '(x) on the left side, and f(x) on the right side

What is the purpose of finding the function (antidiff)?

The purpose of finding the function (antidiff) is to determine the original function from its derivative. In other words, it involves finding the function that, when differentiated, will give the given derivative function.

What is the process of finding the function (antidiff)?

The process of finding the function (antidiff) involves using integration techniques to reverse the process of differentiation. This can include using known integration formulas, substitution, or other methods.

Why is it important to find the function (antidiff)?

It is important to find the function (antidiff) because it allows us to solve problems involving rates of change and to find the original function from its derivative. This can be useful in many areas of science, such as physics, engineering, and economics.

What are some common techniques used to find the function (antidiff)?

Some common techniques used to find the function (antidiff) include the power rule, integration by parts, u-substitution, and trigonometric substitution. It is important to select the appropriate method based on the given derivative function.

Are there any limitations to finding the function (antidiff)?

Yes, there are some limitations to finding the function (antidiff). Not all functions can be antidifferentiated, and some may require more advanced techniques that are not always easy to apply. Additionally, the process of antidifferentiation can lead to an infinite number of possible solutions, so it is important to check for a constant of integration when solving an antidifferentiation problem.