Subscript derivative notation

Otherwise, the answer is missing a term.In summary, the equation At, r = Aφ, r can be solved for At by using the equation Aφ = r4 and substituting it into the original equation. This results in the equivalent equation ∂/∂r (At) = ∂/∂r (r4). To find At, the integral of both sides of the equation is taken with respect to r, resulting in At = r5/5, assuming r and t are independent variables.
  • #1
73
2
I have an equation that looks like

At, r = Aφ, r

If I know that Aφ = r4 , then how do I find At ?

I believe that the above equation is equivalent to: ∂/∂r (At) = ∂/∂r (Aφ) , correct?

Then substitute the value Aφ and we have ∂/∂r (At) = ∂/∂r (r4)

And then to get At I take the integral on both sides? so eventually At = r5/5 ?
 
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  • #2
Abdul.119 said:
I have an equation that looks like

At, r = Aφ, r

If I know that Aφ = r4 , then how do I find At ?

I believe that the above equation is equivalent to: ∂/∂r (At) = ∂/∂r (Aφ) , correct?
Yes, ##A_{t, r}## is notation that means ##\frac{\partial}{\partial r}\frac{\partial A}{\partial t}##
Abdul.119 said:
Then substitute the value Aφ and we have ∂/∂r (At) = ∂/∂r (r4)

And then to get At I take the integral on both sides?
Yes. Integrate with respect to r.
Abdul.119 said:
so eventually At = r5/5 ?
Are r and t independent of each other. If so, the above looks fine.
 

1. What is subscript derivative notation?

Subscript derivative notation is a way of representing the derivative of a function using subscripts. It is commonly used in mathematics and physics to denote the partial derivative of a multivariable function with respect to a specific variable.

2. How is subscript derivative notation different from regular derivative notation?

Subscript derivative notation differs from regular derivative notation in that it uses subscripts to indicate which variable the derivative is being taken with respect to. Regular derivative notation uses a prime symbol (') or the symbol d/dx to represent the derivative.

3. Can subscript derivative notation be used for any type of derivative?

Yes, subscript derivative notation can be used for any type of derivative, including partial derivatives, total derivatives, and higher order derivatives.

4. How do you read subscript derivative notation?

To read subscript derivative notation, you start by reading the function name, followed by a comma and the variable that the derivative is being taken with respect to. For example, if you see fx, you would read it as "the partial derivative of f with respect to x."

5. What are the benefits of using subscript derivative notation?

Subscript derivative notation is beneficial because it clearly indicates which variable the derivative is being taken with respect to, making it easier to understand and interpret. It also allows for the representation of multiple derivatives in a compact and concise manner.

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