What is the difference between f'(x), y', and dy/dx?
Just notation.
they mean the same thing.
I say tomato, you say "to-maato"
If y is the dependent variable and x the independent variable, they are all the same.
The minor syntaxical differences are
1. in f'(x), the variable y is not necessary, as f(x) takes the place of y.
2. in y' (Newton's notation), the independent variable is understood according to context. If there is no other information, it would probably be x.
3. dy/dx (Leibniz notation) This is the explicit form with no ambiguities.
The notations f'(x), y', and dy/dx are all commonly used in calculus to denote the derivative of a function. Although they might appear slightly different, they all refer to the same concept.
To understand the difference between these notations, it's important to know that "f(x)" is a function that describes the relationship between an independent variable "x" and a dependent variable "y." The derivative represents the rate at which the dependent variable changes with respect to the independent variable.
1. "f'(x)": This notation denotes the derivative of the function f(x) with respect to x. It is read as "f prime of x." The prime symbol indicates that we are taking the derivative of the function.
2. "y'": This notation is used when the dependent variable is written as "y" instead of "f(x)". It represents the derivative of y with respect to the independent variable x. So, "y prime" is equivalent to "dy/dx."
3. "dy/dx": This notation is often referred to as "dy by dx" or "differential y by differential x." It represents the derivative of the dependent variable y with respect to the independent variable x.
In summary, f'(x), y', and dy/dx are different notations for the same concept of the derivative. The choice of notation depends on the context and personal preference.