deriv

default(realprecision,38);
sin'(4)
sin'(1+I)
sin'(x)
derivnum(x=4,sin(x))
derivnum(x=t^2+O(t^4),sin(x))
derivnum(x=t,sin(x))
derivnum(x=1/(1+t),sin(x))
derivnum(x=1,Pi^x)
v=[Mod(x*y+1,x^2+1), Mod(1,3), ffgen(2^3,'t), 1+x*y+O(x^3), x/(x+y), (x^3/3+x+1) / (x^2+1)^2, [x*y], Mat(x*y)];
{
for (i=1,#v,
  my(u=v[i]);
  print(deriv(u,'x));
  print(u');
  print(derivn(u,2,'x));
  print(deriv(u,'y));
  print(derivn(u,2,'y));
  iferr(print(intformal(u,'x)),E,print(E));
  iferr(print(intformal(u,'y)),E,print(E));
)
}
intformal(1-A,Y)
a=intformal(Pol(0,x), y)
b=intformal(Pol(0,y), x)
variable(a)
variable(b)
a=intformal(O(x), y)
b=intformal(O(y), x)
variable(a)
variable(b)

f(x) = (x^2+x)*'y;
f'(1)
f''(1)
derivn(f,2)(1)

derivnum(x=0,1/(x^2+1),2)
derivnum(x=2.0,1/(x^2+1),2)
derivnum(x=1+I,1/(x^2+1),2)
derivnum(x=t,1/(x^2+1),2)
derivnum(x=1/t,1/(x^2+1),2)
derivnum(x=0,exp(sin(x)),16)
round( derivnum(x=0,exp(sin(x)),[0..13]) )
derivnum(t=0,1,[]) \\ #2216
derivnum(t=x^2,exp(t),4)
derivnum(t=x^2+O(x^20),exp(t),4)
derivnum(z=0,0,0)

\\ #2162
deriv(2/(4*x^2+1),x)

\\ ERORS
derivnum(z=0,0,[0,-1])
derivnum(z=0,0,[1,-1])
derivnum(z=0,0,x)
derivn(cos,-1)
derivn(cos,1,'x)
sin'("")
sin''("")
(x->x)'("")
(x->x)''("")