PARTIAL DERIVATIVE Meaning and
Definition
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A partial derivative refers to the derivative of a multi-variable function with respect to one of its individual variables, while holding all other variables constant. It measures the rate of change of the function when only one variable varies, while the others are kept fixed.
In a mathematical sense, given a function f(x₁, x₂, ..., xn) with n independent variables, the partial derivative of f with respect to the variable xᵢ, denoted as ∂f/∂xᵢ or fᵢ, is calculated by differentiating the function with respect to xᵢ while considering other variables as constants. The partial derivative fᵢ represents the slope of the function in the direction of xᵢ, indicating the rate of change of the function along that specific variable.
Partial derivatives play a crucial role in mathematical analysis, physics, and engineering, allowing for an understanding of how a multi-variable function changes due to variations in its different variables. They are particularly valuable in optimization, where determining the critical points of a function's partial derivatives helps identify maximum and minimum values.
Partial derivatives can be further extended to higher-order derivatives, where multiple partial derivatives of different orders are taken. This process involves differentiating the function repeatedly, considering specific variables each time, and is used to analyze more complex behaviors and relationships within mathematical models.
Common Misspellings for PARTIAL DERIVATIVE
- oartial derivative
- lartial derivative
- -artial derivative
- 0artial derivative
- pzrtial derivative
- psrtial derivative
- pwrtial derivative
- pqrtial derivative
- paetial derivative
- padtial derivative
- paftial derivative
- pattial derivative
- pa5tial derivative
- pa4tial derivative
- parrial derivative
- parfial derivative
- pargial derivative
- paryial derivative
- par6ial derivative
- par5ial derivative
Etymology of PARTIAL DERIVATIVE
The term "partial" in "partial derivative" refers to the fact that a partial derivative measures the rate of change of a function with respect to one variable, while holding other variables constant.
The word "derivative" is derived from Latin, with "derīvātus" being the past participle of "derīvāre", which means "to derive". It was used in mathematics to refer to the process of finding the derivative of a function.
So, the term "partial derivative" is a combination of "partial" from Latin "partialis", meaning "a part of", and "derivative" from Latin "derīvāre", meaning "to derive". Together, it represents the concept of measuring the rate of change of a function with respect to one variable while keeping other variables constant.
Similar spelling words for PARTIAL DERIVATIVE
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