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Cinitiator
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Homework Statement
What does it mean when lowercase Delta (δ) is used in partial derivative and derivative notation? Does it make any difference? Or is it just a personal preference?
Homework Equations
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The Greek character δ (lower-case Delta) is not used in either kind of derivative. In ordinary derivatives, d is used, as in $$\frac{dy}{dx}$$Cinitiator said:Homework Statement
What does it mean when lowercase Delta (δ) is used in partial derivative and derivative notation? Does it make any difference? Or is it just a personal preference?
Homework Equations
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The Attempt at a Solution
HallsofIvy said:If you means something like [itex]\delta x[/itex] or [itex]\delta f[/itex], it means "a slight change in" x or f. It does NOT occur in "partial derivative and derivative notation" but you may see it in the definition of the derivative.
The Δ symbol in derivative notation represents the change in a function's value over a specific interval. The partial derivative notation, on the other hand, uses the ∂ symbol to indicate the change in a function with respect to a specific variable while holding all other variables constant.
To calculate a derivative using Δ, you would divide the change in the function's value by the change in the independent variable. This is known as the average rate of change and can be used to approximate the derivative at a specific point.
Partial derivatives are used to analyze how a function changes with respect to one variable while holding all other variables constant. This is particularly useful in multivariable calculus and optimization problems.
No, Δ can only be used for functions with one independent variable. For functions with multiple independent variables, partial derivatives are used to analyze the change in the function with respect to each variable.
To notate higher order derivatives using Δ, you would use the notation Δy/Δx^n, where n represents the order of the derivative. For example, a second order derivative would be notated as Δ^2y/Δx^2.