derivative calculator
calculators operate in digital numbers
the derivative is a numeric proportion or rate
calculators can specify derivatives by digital numbers
By adding another number to each precise-real number -
infinitesmals, rather than complex imaginary-parts -
we can have calculators compute derivatives:
the second number is the slope at the precise-real number,
thus sin(pi/2) = 1.0000000000 ,
and its second number, its derivative, is 0.0000000000 = cos(pi/2) .
Calculations can follow the derivative chain-rules,
eg. for finitesmal a,b and infinitesmals d,e representing
their corresponding [cumulated] slopes
- 2(a+d) = (2a)+(2d)
- (a+d)*(b+e) = (ab)+(ae+bd) : (de) being doubly infinitesmal
- sin(a+d) = sin(a)+cos(a)*d : cos(d) being about 1-(d^2/2),
and sin(d) about (d)-(d^3/6) - multiply infinitesmally
indistinguishable from their first terms
- etc.
Although this accommodates only common single-parametrized
variables, each calculation can be re-done with
adjustments to identify sensistivity to other parameters.
© 1996 GrandAdmiralPetry@Lanthus.net