partial derivative Synonyms

No Synonyms and anytonyms found

partial derivative Meaning

Wordnet

partial derivative (n)

the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant

partial derivative Sentence Examples

1. The partial derivative of the function f(x, y) with respect to x is given by ∂f/∂x.
2. The partial derivative of the function g(u, v, w) with respect to u is denoted as ∂g/∂u.
3. In fluid dynamics, the partial derivatives of the velocity field with respect to space coordinates are used to represent the velocity gradient tensor.
4. In thermodynamics, the partial derivative of a thermodynamic potential with respect to one of its natural variables represents the corresponding extensive property.
5. The mixed partial derivative of the function h(x, y, z) with respect to x and y is defined as ∂²h/∂x∂y.
6. The partial derivative of the function f(x, y) with respect to y, while holding x constant, is written as (∂f/∂y)x.
7. The partial derivative of the function g(r, θ, φ) with respect to the radial coordinate r is given by ∂g/∂r.
8. In economics, the partial derivative of a utility function with respect to a particular good represents the marginal utility of that good.
9. The partial derivative of the function h(x, y, z) with respect to z, while holding x and y constant, is denoted as ∂h/∂z(x, y).
10. The partial derivatives of a vector-valued function with respect to different variables form the Jacobian matrix of the function.

FAQs About the word partial derivative

What is the meaning of the word partial derivative

the derivative of a function of two or more variables with respect to a single variable while the other variables are considered to be constant

What are the synonyms of the word partial derivative

No synonyms found.

What are the antonyms of the word partial derivative

No antonyms found.

What is the usage of word partial derivative

The partial derivative of the function f(x, y) with respect to x is given by ∂f/∂x.

The partial derivative of the function g(u, v, w) with respect to u is denoted as ∂g/∂u.

How to use the word partial derivative in a sentence?

In fluid dynamics, the partial derivatives of the velocity field with respect to space coordinates are used to represent the velocity gradient tensor.

In thermodynamics, the partial derivative of a thermodynamic potential with respect to one of its natural variables represents the corresponding extensive property.