what is partial differentiation
Answers
Answer: It is used to find the local behavior of a multivariable function.
Step-by-step explanation:
Partial differentiation is a method of finding the rate of change of a function with respect to one of its variables, while holding all the other variables constant. It is used to find the local behavior of a multivariable function.
For example, consider a function z = f(x,y), where z is a function of two variables x and y. To find the partial derivative of z with respect to x, we treat y as a constant and find the rate of change of z with respect to x. Similarly, to find the partial derivative of z with respect to y, we treat x as a constant and find the rate of change of z with respect to y.
The partial derivative of a function with respect to x is represented as ∂f/∂x, and the partial derivative of a function with respect to y is represented as ∂f/∂y.
Partial derivatives are used in many fields such as physics, engineering and economics, to analyze the behavior of a system and to make predictions about how the system will change in response to changes in the input variables.
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