1 | initial version |
Hi,
In Sage, the syntax diff(g,x,m)
where x
and m
are two symbolic variables, does not stand for the m
-th derivative of g
with respect to x
, but for the second order partial derivative of g
with one derivative taken with respect to x
and the other one with respect to m
, i.e. in LaTeX notation \frac{\partial^2 g}{\partial x \partial m}. This explains why example 1 returns 0 (m
does not appear in g
), while example 2 returns something nonzero ((x^2-1)^n
is a function of both x
and n
).
If, instead of a symbolic variable, the third argument of diff
is a non-negative integer m
, then the outcome is the m
-th derivative of g
with respect to x
: for instance
sage: g = x^2 + 3/2*(x^2 - 1)*x
sage: m = 3 # m is now an integer, not a symbolic variable
sage: diff(g, x, m)
9