Partial differentiation has meaning in the context of the differentiation
of functions of several variables. For example let f(x,y,z) be a function
of x,y,z. The first order partial derivative of f with respect to x
is deined as
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By differentiating these functions again with respect to x, y, or z we obtain the higher order partial derivatives such as
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Chain Rule
Let F be a continuously differentiable function of f,g,h and suppose that each f,g,h is a continuously differentiable function of x,y,z. Then it may be shown that F is a continuously differentiable function of x,y,z and that
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