Defining Derivatives
You can define the derivative in
Mathematica of a function
of one argument simply by an assignment like
.
This defines the derivative of
to be
. In this case, you could have used
instead of
.
The rule for
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
is used.
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This defines the second derivative of
, 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.
| 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
with respect to its second argument.
This uses the definition just given.
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