Re:Exact numeric nth derivatives
by jliszka on Thursday October 24, 2013 @02:59PM
(#6607177)
You're right, it is begging the question, for any simple function, you basically have to tell it what all the derivatives are for it to work.
The power of this technique is that it handles the product rule and chain rule for you, so composition and multiplication of functions work automatically without extra work.
For the case of 1/(1-x), you only need to tell it the derivatives (wrt x) of
f(x, a) = x * a
g(x, a) = x + a
h(x) = 1/x
Then it automatically knows how to compute the derivatives of h(g(f(x, -1), 1)).
The power of this technique is that it handles the product rule and chain rule for you, so composition and multiplication of functions work automatically without extra work.
For the case of 1/(1-x), you only need to tell it the derivatives (wrt x) of
f(x, a) = x * a
g(x, a) = x + a
h(x) = 1/x
Then it automatically knows how to compute the derivatives of h(g(f(x, -1), 1)).