# How to prove this differential expression

• transgalactic
In summary, the conversation is discussing how to prove the correctness of an expression involving derivatives. The suggestion is to use the Liebniz product rule and possibly a proof by induction.
transgalactic
i need to prove that this expression is correct

http://img216.imageshack.us/my.php?image=23051510gd6.gif

f'(x)=d(f(x))/dx
there is no such structure on the left side of the equation
there are a defferential in the power of n
only the d^n??

The first thing I would try is the Liebniz product rule:

$$\frac{d^n}{dx^n}(fg) = \sum_{k=0}^n \frac{n!}{k!(n-k)!}f^{(k)}g^{(n-k)}$$

where $f^{(j)}$ is the jth derivative of f. See if that gets you anywhere.

... or maybe a proof by induction.

Last edited by a moderator:
Last edited by a moderator:

## 1. How do you identify a differential expression?

A differential expression is a mathematical equation that involves differentials, or derivatives of a function. It is typically written in the form of f'(x), where f(x) is the original function.

## 2. What is the process for proving a differential expression?

The process for proving a differential expression involves using various mathematical techniques, such as the chain rule, product rule, and quotient rule, to manipulate the equation until it matches a known derivative. This can also involve solving for the original function using integration.

## 3. Can a differential expression be proven using only algebraic methods?

No, differential expressions require the use of calculus to be proven. Algebraic methods alone are not sufficient to manipulate and solve these types of equations.

## 4. Are there any tips for proving a differential expression?

One tip for proving a differential expression is to always start by identifying the type of expression you are working with (e.g. polynomial, trigonometric, exponential). This will help guide you towards the appropriate mathematical techniques to use.

## 5. Can differential expressions be proven using software or calculators?

While software and calculators can help with the calculations involved in proving a differential expression, the actual proof must be done by hand using mathematical principles. Relying solely on technology to prove a differential expression is not considered a valid scientific method.

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