3.5.5 Defining DerivativesYou can define the derivative in Mathematica of a function f of one argument simply by an assignment like f'[x_] = fp[x]. This defines the derivative of  to be  . In this case, you could have used = instead of :=. The rule for f'[x_] is used to evaluate this derivative.
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Differentiating again gives derivatives of  .
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This defines a value for the derivative of  at the origin.
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The value for g'[0] is used.
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This defines the second derivative of g, with any argument.
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The value defined for the second derivative is used.
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To define derivatives of functions with several arguments, you have to use the general representation of derivatives in Mathematica.
Defining derivatives. This defines the second derivative of g with respect to its second argument. This uses the definition just given.
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