import sympy as sym
x = sym.symbols('x')
expr = sym.cos(3*x)-4*sym.cos(x)**3
print(sym.simplify(expr))
expr = (x**3+x**2-x-1)/(x**2+2*x+1)
print(sym.simplify(expr))
f, g = sym.symbols('f, g', cls=sym.Function)
expr = f(g(x))
print(sym.simplify(sym.diff(expr, x)/sym.diff(g(x), x)))