Partial Derivatives of Functions of More than one independent variable
In a Nut Shell: The derivative of a function of one independent variable (say x)
relates directly to the slope of the dependent variable (say y). i.e. dy/dx
Likewise for function z of two independent variables (say x and y), the partial
derivative on x gives the slope in the x-direction and the partial derivative on y gives
the slope in the y direction. i.e. ∂z/∂x and ∂z/∂y The notion of partial derivatives
holds for functions of any number of independent variables.
Let’s start by reviewing the situation of a function of only one independent variable, x.
Recall the definition of the derivative for a function of one independent variable, x
f ’(x) = lim [ f(x + h) - f(x)]/ h
h à 0
With one independent variable, f ’(x) represents the slope of the curve f(x) at point P.
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