Chapter 2: Differentiation
Section 2.4: The Chain Rule
Example 2.4.6
Use the Chain rule to obtain the derivative of the composite function .
Solution
Apply the Chain rule
Obtain a Maple solution
Control-drag Context Panel: Assign Function
Write
Context Panel: Evaluate and Display Inline
=
Maple uses the D-operator to represent differentiation of functions. The object is the function , so it is evaluated at , the "stuff inside;" similarly for , the function , which is evaluated at , the "stuff inside ."
Thus, Maple knows how to implement the Chain rule, but it uses the compact D-operator notation.
Solution using the operator
The vertical stroke means "evaluated at" and its use in the first set of parentheses is the equivalent of writing, for example, . Use of the prime for differentiation generally results in much more compact expressions.
Maple's implementation of the operator
Maple uses twice, the first time for ; and the second, for .
Again, Maple knows the differentiation rules, but the notation it uses to express them can sometimes require an explanation.
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