Curly d vs Normal d: Derivatives Explained

In summary, curly d is used for partial derivatives and regular d is used for total derivatives. Partial derivatives only consider one variable as a variable and keep the rest as constants, while total derivatives also take into account the relationship between variables. The curly d is commonly used for partial derivatives, but it can also be used for other purposes.
  • #1
roberto85
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Homework Statement


The title says it all, what is the difference between the curly d used for derivatives and a normal d in derivatives. When do you know when to use each one? Thanks
 
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  • #2


roberto85 said:

Homework Statement


The title says it all, what is the difference between the curly d used for derivatives and a normal d in derivatives. When do you know when to use each one? Thanks

Curly d is used for partial derivatives. Regular d is for a total derivative.

Partial derivatives are when treat one variable as a variable and keep the rest as constants ignoring the relationship between the variables.

Total derivatives are when you do the same as above but the relationship between variables remains.
 
  • #3


Sorry! said:
Curly d is used for partial derivatives. Regular d is for a total derivative.

Partial derivatives are when treat one variable as a variable and keep the rest as constants ignoring the relationship between the variables.

Total derivatives are when you do the same as above but the relationship between variables remains.

Thanks, i did remember the curly d being used a lot in partial deriv's, but wasnt sure that was their sole use. Thanks for clearing it up
 

1. What is the difference between Curly d and Normal d when talking about derivatives?

Curly d and Normal d both refer to the symbol used to represent a derivative in mathematics. The main difference is that Curly d is typically used to represent a partial derivative, while Normal d is used to represent a regular derivative. A partial derivative is a derivative with respect to one variable while holding all other variables constant. A regular derivative is a derivative with respect to a single variable.

2. How do you calculate a derivative using Curly d vs Normal d?

The process for calculating a derivative using Curly d and Normal d is the same. You take the derivative with respect to the given variable and plug it into the appropriate formula. The only difference is that with Curly d, you may have to specify which variable you are taking the derivative with respect to, while with Normal d, it is assumed to be the variable used in the function.

3. Can you use Curly d and Normal d interchangeably?

No, you cannot use Curly d and Normal d interchangeably. As mentioned earlier, Curly d is used for partial derivatives while Normal d is used for regular derivatives. Using the wrong symbol can lead to incorrect calculations and results. It is important to use the correct symbol depending on the type of derivative you are calculating.

4. When is it appropriate to use Curly d instead of Normal d?

Curly d is used when dealing with functions of multiple variables. For example, if you have a function f(x,y) where x and y are both variables, you would use Curly d to represent the partial derivative of f with respect to x or y. In this case, using Normal d would not make sense as it would not specify which variable you are taking the derivative with respect to.

5. Are there any other symbols used to represent derivatives?

Yes, there are other symbols used to represent derivatives, such as d/dx, dy/dx, and ∂/∂x. These symbols also indicate the derivative with respect to a given variable. However, Curly d and Normal d are the most commonly used symbols for derivatives, with Curly d specifically used for partial derivatives and Normal d used for regular derivatives.

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