Chapter 4: Partial Differentiation
Section 4.2: Higher-Order Partial Derivatives
Example 4.2.1
If and , obtain all second partial derivatives, both at and at .
Solution
Mathematical Solution
Table 4.2.1(a) lists the simplified forms of the second partial derivatives of , both at and at .
Partial
at
Table 4.2.1(a) Second partials of at and
Maple Solution - Interactive
Define as an expression and use the second-partial operators from the Calculus palette.
Control-drag
Context Panel: Assign Name
Second partial derivatives at
Calculus palette: Second-partials operators
Context Panel: Evaluate and Display Inline
Context Panel: Simplify≻Simplify
=
Expression palette: Evaluation template
Alternatively, define the second partial derivatives as functions. Every subscripted name must be an Atomic Identifier.
Calculus palette: Second-partial operators
Context Panel: Assign Function
Obtain the second partial derivatives at
Maple Solution - Coded
If is an expression, the simplified forms for its four second partial derivatives are obtained with the simplify and diff commands. Evaluation at is obtained with the eval command. The names to which the derivatives have been assigned are all Atomic Identifiers.
Assign the expression to the name .
Second partials at
If is a function, the simplified forms for its four second partial derivatives are obtained with the simplify command applied to the D-operator. Evaluation at is immediate since the D-operator returns derivatives as functions.
Define the function .
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