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The derivative represents the slope of a function. It can also represent the instantaneous velocity. The second derivative represents the acceleration and can also represent the concavity of a function.
In order to calculate these and any other higher order derivative in Maple the commands **D** and **diff** are used. For the function
the second and third derivative will be calculated using both commands.
> f:=x->7*x^3-sin(x)^3;
> plot(f(x), x=-2..2);
> (D@@2)(f)(x);
> D[1,1](f)(x);
> diff(f(x),x,x);
> diff(f(x),x$2);

The 2 in the first **D** command stands for the second derivative. The 1 in the second **D** command means ``with respect to x''.
> (D@@3)(f)(x);
> D[1,1,1](f)(x);
> diff(f(x),x,x,x);
> diff(f(x),x$3);

In order to substitute an value into the higher order derivative the **subs** command must be used for **diff**; but for **D** the value can be incorporated into the command itself.
> evalf(subs(x=0,diff(f(x),x,x,x)));
> (D@@3)(f)(0);
> D[1,1,1}(f)(0);

Remember from your work with the first derivative that the **D** command cannot be used with expressions.
> g:=19*x^5-14*x+100;
> D(g)(x);
> diff(g,x);

*Jane E Bouchard *

2005-02-01