Operator D vs. Function diff - Maple Help

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Operator D vs. Function diff

Description

 • The D operator computes derivatives of operators, while diff computes derivatives of expressions.
 • The argument and result of D are functional operators, while the argument and result of diff are expressions.
 • The following diagram illustrates the transitions that occur using D, diff, unapply, and function application.

 function application --> f   -----------------------------   f(x) <-- unapply |                                    | |                                  d | ^ |                                  i | | |D()                               f | | |                                f | i | |                                  | n | V                                | | t |                                  V | |                                    | function application --> D(f) ----------------------------   f'(x) <-- unapply

Examples

 > $\mathrm{D}\left(\mathrm{sin}\right)\left(x\right)$
 ${\mathrm{cos}}{}\left({x}\right)$ (1)
 > $\frac{ⅆ}{ⅆx}\mathrm{sin}\left(x\right)$
 ${\mathrm{cos}}{}\left({x}\right)$ (2)
 > $\mathrm{D}\left(f@g\right)$
 ${\mathrm{D}}{}\left({f}\right){@}{g}{}{\mathrm{D}}{}\left({g}\right)$ (3)
 > $\frac{ⅆ}{ⅆx}f@g\left(x\right)$
 ${\mathrm{D}}{}\left({f}\right){}\left({g}{}\left({x}\right)\right){}\left(\frac{{ⅆ}}{{ⅆ}{x}}{}{g}{}\left({x}\right)\right)$ (4)
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