What is dy/dx and how does it relate to derivatives?

[vanmaiden]

the meaning of "dy/dx

Homework Statement

I am unsure of what dy/dx means when used in derivatives. However, I do know that it is called the derivative operator and have been told its the derivative of y relative to x, but could someone elaborate this for me?

Homework Equations

an example equation might be dy/dx = x² + 4x + 4

The Attempt at a Solution

I have been told that its called the derivative operator and that it is the derivative of y relative to x.

 

[vanmaiden]

I wasn't too sure if this would be considered a homework question. If someone could let me know so I can start posting in the correct section, that would be helpful.

 

[Mark44]

Homework Statement

I am unsure of what dy/dx means when used in derivatives. However, I do know that it is called the derivative operator and have been told its the derivative of y relative to x, but could someone elaborate this for me?

Homework Equations

an example equation might be dy/dx = x² + 4x + 4

The Attempt at a Solution

I have been told that its called the derivative operator and that it is the derivative of y relative to x.

dy/dx is the derivative of y with respect to x, where y is assumed to be a differentiable function of x.

dy/dx is not an operator - it is a function. d/dx is an operator that is applied to a differentiable function. A function takes a number as its input, and produces a number as its output. In contrast, an operator takes a function as its input, and produces a function as its output.

 

[vanmaiden]

dy/dx is the derivative of y with respect to x, where y is assumed to be a differentiable function of x.

dy/dx is not an operator - it is a function. d/dx is an operator that is applied to a differentiable function. A function takes a number as its input, and produces a number as its output. In contrast, an operator takes a function as its input, and produces a function as its output.

To get my terminology straight, would a differential function be a derivative? please elaborate. Thank you.

 

[Mark44]

To get my terminology straight, would a differential function be a derivative? please elaborate. Thank you.

Do you mean "differentiable" function? If so, that's a function that can be differentiated; i.e., one that has a derivative. A differential is something different.

 

[vanmaiden]

Do you mean "differentiable" function? If so, that's a function that can be differentiated; i.e., one that has a derivative. A differential is something different.

Yes, exactly what I meant. Thank you

 

[Mark44]

There's something of a disconnect in the terminology that is used in English. To get the derivative of a function, we differentiate it (we don't derive it). If the function has a derivative, it is differentiable (not derivable). Go figure.

 

[Dickfore]

That's because the concept of a differentiable function for functions with more than variable is more stringent than the simple existence of the partial derivatives.

 

[vanmaiden]

There's something of a disconnect in the terminology that is used in English. To get the derivative of a function, we differentiate it (we don't derive it). If the function has a derivative, it is differentiable (not derivable). Go figure.

Fascinating. Therefore, what would one consider deriving a function?

 

[Mark44]

In the context of this thread (differentiation and the derivative), "deriving a function" has no meaning.

In a different context, one can start from observations and derive a general formula, but this is unrelated to differentiation.

 

[vanmaiden]

Though my question was off-topic, thank you for answering it anyway.