definition of a partial derivative
fx(x,y)=[f(x+h, y)-f(x,y)]/h
A partial derivative is a mathematical concept used in calculus to describe how much a function changes when only one of its variables is changed. Specifically, it measures the rate of change of the function with respect to one of its variables, while holding all other variables constant.
Formally, if we have a function f(x, y), then the partial derivative of f with respect to x (denoted by ∂f/∂x or fx) measures the rate of change of f when only the variable x is allowed to vary, while the variable y is held constant. Similarly, the partial derivative of f with respect to y (denoted by ∂f/∂y or fy) measures the rate of change of f when only the variable y is allowed to vary, while x is held constant.
Partial derivatives are useful in many fields of mathematics and science, including physics, economics, and engineering, for analyzing the behavior of complex systems and predicting their future outcomes.
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