When can one Change order of derivatives?

Thread starter Charanjit
Start date Jan 16, 2012
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Change Derivatives

In summary, changing the order of derivatives is done for the purpose of simplifying calculations or solving problems more easily. It is necessary in cases where the original order is too complex. Common methods for changing the order include using the chain rule, product rule, and quotient rule. However, changing the order can affect the final result and there are limitations to this process, such as not always being possible or resulting in a simpler calculation.

Jan 16, 2012

Charanjit

Here is an example...

d/dz(dp/dx) = d/dx(dp/dz)

I don't remember learning this in my calculus or differential equations classes unless it was called something else.

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Jan 16, 2012

Simon Bridge

Science Advisor

Homework Helper

Those would be mixed partial derivatives.
Look it up.

The short answer is: almost always.

Last edited: Jan 16, 2012

Jan 16, 2012

Charanjit

Hmm...ok never knew that. Thanks.

1. What is the purpose of changing the order of derivatives?

The purpose of changing the order of derivatives is to simplify the calculation of a derivative or to make it easier to solve a problem. Sometimes, changing the order of derivatives can also help to reveal patterns or relationships between different variables.

2. When is it necessary to change the order of derivatives?

It is necessary to change the order of derivatives when the original order is too complex or difficult to solve. This is often the case when dealing with higher order derivatives or when trying to solve a problem that involves multiple variables.

3. What are some common methods for changing the order of derivatives?

Some common methods for changing the order of derivatives include using the chain rule, the product rule, and the quotient rule. These rules allow us to rearrange the terms in a derivative and simplify the calculation.

4. Can changing the order of derivatives affect the final result?

Yes, changing the order of derivatives can affect the final result. It is important to be careful when changing the order of derivatives, as it can sometimes lead to incorrect solutions if not done correctly.

5. Are there any limitations to changing the order of derivatives?

Yes, there are limitations to changing the order of derivatives. In some cases, it may not be possible to change the order of derivatives without altering the original equation or problem. Additionally, changing the order of derivatives may not always result in a simpler or easier calculation.