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Simtel MSDOS - Coast to Coast
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D.(X)
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1993-11-15
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# d(f(x),x) differentiates f(x) with respect to x. f'(x) = d(f(x),x).
# d(f(x), x,n) differentiates f(x) with respect to x in n order
sign'(x_) := 0
abs'(x_) := abs(x)/x
ln'(x_) := 1/x
exp'(x_) := e^x
sin'(x_) := cos(x)
cos'(x_) := -sin(x)
#tan'(x_) := sec(x)^2
#cot'(x_) := -csc(x)^2
#sec'(x_) := tan(x)*sec(x)
#csc'(x_) := -cot(x)*csc(x)
#asin'(x_) := 1/sqrt(1-x^2)
#acos'(x_) := -1/sqrt(1-x^2)
#atan'(x_) := 1/(1+x^2)
#acot'(x_) := -1/(1+x^2)
#asec'(x_) := 1/(x*sqrt(x^2-1))
#acsc'(x_) := -1/(x*sqrt(x^2-1))
#sinh'(x_) := cosh(x)
#cosh'(x_) := sinh(x)
#tanh'(x_) := sech(x)^2
#coth'(x_) := -csch(x)^2
#sech'(x_) := -tanh(x)*sech(x)
#csch'(x_) := -coth(x)*csch(x)
#asinh'(x_) := 1/sqrt(1+x^2)
#acosh'(x_) := 1/sqrt(x^2-1)
#atanh'(x_) := 1/(1-x^2)
#acoth'(x_) := 1/(x^2-1)
#asech'(x_) := -1/(x*sqrt(1-x^2))
#acsch'(x_) := -1/(x*sqrt(1+x^2))
si'(x_) := sin(x)/x
ci'(x_) := cos(x)/x
erf'(x_) := 2/sqrt(pi)*exp(-x^2)
gamma'(x_) := gamma(x)*polygamma(x)
ei'(x_) := e^x/x
li'(x_) := 1/ln(x)
d(gamma(n_, x_), x) := x^n*e^-x
d(ei(n_, x_), x_) := x^n*e^x
d(li(n_, x_), x_) := ln(x)^n
d(y_, x_,n_) := if(n>0, block(p:=y, do(p:=d(p,x), j,1,n,1), p, local(p) ))