5 Questions
Explain the concept of a partial derivative in mathematics.
A partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant. It can be thought of as the rate of change of the function in a specific direction.
Who is credited with creating the modern partial derivative notation?
The modern partial derivative notation was created by Adrien-Marie Legendre in 1786, although he later abandoned it; Carl Gustav Jacob Jacobi reintroduced the symbol in 1841.
What is the notation used to denote partial derivatives?
The symbol used to denote partial derivatives is $\partial$. The partial derivative of a function $f(x, y, ...)$ with respect to the variable $x$ is denoted as $\frac{\partial f}{\partial x}$ or $\partial_x f$.
When was the symbol $\partial$ first used in mathematics?
One of the first known uses of the symbol $\partial$ in mathematics is by Marquis de Condorcet in 1770, who used it for partial differences.
What is the definition of a partial derivative?
Like ordinary derivatives, the partial derivative is defined as a limit, representing the rate of change of a function with respect to one of its variables while holding the others constant.
Study Notes
Partial Derivatives in Mathematics
- A partial derivative is a derivative of a function of multiple variables when all but one of the variables are held constant, and the rate of change of the function with respect to that one variable is measured.
History of Partial Derivative Notation
- The modern partial derivative notation is credited to Leonhard Euler, an 18th-century Swiss mathematician.
Notation for Partial Derivatives
- The notation used to denote partial derivatives is ∂, which is a stylized letter "d" that distinguishes partial derivatives from ordinary derivatives.
Origin of the ∂ Symbol
- The symbol ∂ was first used in mathematics by the German mathematician Johann Friedrich Pfaff in 1788.
Definition of Partial Derivative
- The partial derivative of a function f(x, y, ...) with respect to one of its variables x is defined as the limit of the difference quotient as the change in x approaches zero, while the other variables are held constant.
Test your understanding of partial derivatives with this quiz. Partial derivatives are crucial in fields such as vector calculus and differential geometry, and this quiz will help you reinforce your knowledge and skills.
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