Chapter 2: Differentiation
Section 2.4: The Chain Rule
Use the Chain rule to obtain the derivative of the composite function Fx=fghx.
Apply the Chain rule
Obtain a Maple solution
Context Panel: Assign Function
Fx=fghx→assign as functionF
Context Panel: Evaluate and Display Inline
F′x = D⁡f⁡g⁡h⁡x⁢D⁡g⁡h⁡x⁢ⅆⅆx⁢h⁡x
Maple uses the D-operator to represent differentiation of functions. The object Df is the function f′, so it is evaluated at ghx, the "stuff inside;" similarly for Dg, the function g′, which is evaluated at hx, the "stuff inside g."
Thus, Maple knows how to implement the Chain rule, but it uses the compact D-operator notation.
Solution using the operator ddx
The vertical stroke means "evaluated at" and its use in the first set of parentheses is the equivalent of writing, for example, f′ghx. Use of the prime for differentiation generally results in much more compact expressions.
Maple's implementation of the operator ddx
Maple uses t1 twice, the first time for v=ghx; and the second, for w=hx.
Again, Maple knows the differentiation rules, but the notation it uses to express them can sometimes require an explanation.
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