Rewriting Equations with Derivatives: A Quick Guide

Thread starter Jess1986
Start date Mar 28, 2006

In summary, rearranging equations allows us to manipulate mathematical expressions in order to solve for a different variable or to simplify the equation. It is necessary when we need to solve for a specific variable or when the equation is too complicated to solve in its current form. The general steps to rearrange an equation are: 1) Identify the variable that you want to solve for; 2) Isolate that variable on one side of the equation using inverse operations; 3) Simplify the equation as much as possible; 4) Check your answer by plugging it back into the original equation. In general, most types of equations can be rearranged as long as they follow the basic rules of algebra. However, some equations may be more

Mar 28, 2006

Jess1986

Show that m(2r'a' +ra'')=0 can be rewritten as md/dt(r^2*a')=0

Has anyone got any tips on how i should go about this?? Thanks x

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Mar 28, 2006

Doc Al

Mentor

Use the product rule to take the derivative.

Mar 28, 2006

TolsePhy

it's trivial. you can jump to the solution directly.

1. What is the purpose of rearranging equations?

Rearranging equations allows us to manipulate mathematical expressions in order to solve for a different variable or to simplify the equation. This can be helpful in solving complex problems or in finding relationships between different variables.

2. How do you know when to rearrange an equation?

Rearranging an equation is necessary when we need to solve for a specific variable or when the equation is too complicated to solve in its current form. It is important to identify the desired variable and follow the correct steps to rearrange the equation.

3. What are the steps to rearrange an equation?

The general steps to rearrange an equation are: 1) Identify the variable that you want to solve for; 2) Isolate that variable on one side of the equation using inverse operations; 3) Simplify the equation as much as possible; 4) Check your answer by plugging it back into the original equation.

4. Can you rearrange any type of equation?

In general, yes, you can rearrange most types of equations as long as they follow the basic rules of algebra. However, some equations may be more complex and require more advanced techniques for rearranging.

5. Are there any common mistakes to avoid when rearranging equations?

One common mistake to avoid is not performing the same operation on both sides of the equation. This can lead to an incorrect solution. It is also important to pay attention to the order of operations and to keep track of any negative signs when rearranging.