Question

I want to use a function’s derivative in an other function. How should this be done in Maxima?

E.g:

f(x) := 2*x^4;
g(x) := diff(f(x),x)-8;

Now g(x) yields 8x^3-8 as expected, but g(0) gives an error, since diff(f(0),0) doesn’t make sense. But then how should I properly define g?

Answer 1

Michael’s answer is good, but it does the differentiation everytime g(x) is called. (Also, normally you see it wrapped in a block statement to ensure that y is properly localized).

There is a way to force the RHS to evaluate at the time of definition
and with the general x.
The syntax is

(%i1) f(x) := 2*x^4;
                                            4
(%o1)                            f(x) := 2 x
(%i2) g(x) := ''(diff(f(x), x) - 8);
                                          3
(%o2)                          g(x) := 8 x  - 8
(%i3) g(0);
(%o3)                                 - 8

Compare with the block construct:

(%i4) h(x) := block([y], subst([y = x], diff(f(y), y) - 8));
(%o4)        h(x) := block([y], subst([y = x], diff(f(y), y) - 8))
(%i5) h(0);
(%o5)                                 - 8

Notice (%o4) which shows that the RHS is unevaluated.

Ref: http://www.math.utexas.edu/pipermail/maxima/2007/004706.html