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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D[g[x]^2, x] /. x->0
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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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D[g[x]^2, {x, 2}]
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To define derivatives of functions with several arguments, you have to use the general representation of derivatives in Mathematica.
| f'[x_] := rhs | define the first derivative of f | | Derivative[n][f][x_] := rhs | define the n derivative of f |
Derivative[m, n, ... ][g][x_, _, ... ] := rhs
| | define derivatives of g with respect to various arguments |
Defining derivatives. | This defines the second derivative of g with respect to its second argument. | |
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Derivative[0, 2][g][x_, y_] := g2p[x, y]
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| This uses the definition just given. | |
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D[g[a^2, x^2], x, x]
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