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2.6.2. Partial derivatives

Lecture



Let be   2.6.2.  Partial derivatives defined on area D. We assume that the argument y is constant and consider the resulting function in one variable x . Give the variable x an increment Δx . Incrementing Δx will cause the function to increment   2.6.2.  Partial derivatives . The final limit of the ratio of the increment of the function Δz x to the increment of the argument Δx at   2.6.2.  Partial derivatives is called a partial derivative of the first order in x and is denoted by   2.6.2.  Partial derivatives i.e.   2.6.2.  Partial derivatives .

If we consider the argument x constant and consider the function   2.6.2.  Partial derivatives as a function of one variable y , the increment Δy will cause an increment of the function   2.6.2.  Partial derivatives . The final limit of the ratio of the increment of the function Δz y to the increment of the argument Δy at   2.6.2.  Partial derivatives is called a partial derivative of the first order in y and is denoted by   2.6.2.  Partial derivatives i.e.   2.6.2.  Partial derivatives .

The symbols are also used to denote partial derivatives:   2.6.2.  Partial derivatives .

Partial derivatives of the second order of the function   2.6.2.  Partial derivatives are called partial derivatives of its partial derivatives of the first order:   2.6.2.  Partial derivatives .

And   2.6.2.  Partial derivatives if derivatives are continuous.

Derivatives of higher orders are calculated similarly.


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Mathematical analysis. Differential calculus

Terms: Mathematical analysis. Differential calculus