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.
Letís 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 í(x)† =† †lim [ f(x + h)† -†† f(x)]/ h
††††††††††† ††††††††††††††††††††††††††††††††h → 0
With one independent variable,† f í(x) represents the slope of the curve† f(x) at point P.
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