Beispiel 1:

x,y = var('x', 'y')
f(x,y)= exp(x/y)-x
y = function('y')(x)
df = solve(diff(f(x,y), x), diff(y))
pretty_print(expand(df[0]))

Beispiel 2:

x,y = var('x', 'y')
f(x,y)= x + sin(y)
y = function('y')(x)
df = solve(diff(f(x,y), x), diff(y))
pretty_print(df)


Beispiel 3:

f(x) = x^2
fd(x) = f(x).diff()
f2d(x) = fd(x).diff()
k = f2d(x)/(1+fd(x)^2)^(3/2)
print k
kd(x) = k.diff()
k2d(x) = kd.diff()
e = solve(kd(x) == 0, x)
print e
x1 = var('x1')
for i in e:
    x1 = float(i.right())
    print ("d2f(x) = " +str(k2d(x1)))
  
    
g = Graphics()
g += plot(f(x), xmin = -3, xmax = 3, ymin = -5, ymax = 5)
g += plot(k, xmin = -3, xmax = 3, ymin = -5, ymax = 5, color = (0,1,1))