Beispiel 1:


x = var('x')
f(x) = 4*x^3/(2*x^5+5)
d = diff(f(x), x)
print d.simplify_full()



Beispiel 2:

f(x) = sqrt(2*x^5+3)
d = diff(f(x), x)
print d.simplify_full()


Beispiel 3:

f(x) = sqrt(2*x^5+3)
fd(x) = f(x).diff().simplify_full()
pretty_print("f'(x) = ", fd(x))


Beispiel 4:

f(x) = cot(x)*cos(x)
fd(x) = f(x).diff().simplify_full()
pretty_print("f'(x) = ", fd(x))



Beispiel 5:

x = var('x')
f(x) = x*(x+1)*(x-2)
n = solve(f(x) == 0, x)
print ("Nullstellen = " +repr(n))

df(x) = derivative(f(x), x)
print ("1. Ableitung = " +str(df(x).simplify_full()))
e = solve(df(x) == 0, x)
print ("Extremstellen von f = " +repr(e))

d2f(x) = derivative(df(x), x)
print ("2. Ableitung = " +str(d2f(x).simplify_full()))

x1 = var('x1')
for i in e:
    x1 = float(i.right())
    print("d2f(x) = " +str(d2f(x1)))
   
g = Graphics()
g += plot(f(x), xmin = -3, xmax = 3, ymin = -5, ymax = 5)
g += plot(df(x), xmin = -3, xmax = 3, ymin = -5, ymax = 5, color = (0,1,1))

for sln in n:
    g += point((sln.right(), f(sln.right())))
for sln in n:
    g += point((sln.right(), f(sln.right())))
g.show()