import sympy as sym
from IPython.display import display,Math

print('Circular derivatives')
display(Math('\\frac{d}{dx} \\cos(x) = -\\sin(x)'))
display(Math('\\frac{d}{dx} -\\sin(x) = -\\cos(x)'))
display(Math('\\frac{d}{dx} -\\cos(x) = \\sin(x)'))
display(Math('\\frac{d}{dx} \\sin(x) = \\cos(x)'))

display(Math('\\quad \\quad \\leftarrow \\cos(x) \\leftarrow'))
display(Math('-\\sin(x) \\quad \\quad \\quad \\sin(x)'))
display(Math('\\quad \\quad \\rightarrow -\\cos(x)\\rightarrow '))

Circular derivatives

$\displaystyle \frac{d}{dx} \cos(x) = -\sin(x)$

$\displaystyle \frac{d}{dx} -\sin(x) = -\cos(x)$

$\displaystyle \frac{d}{dx} -\cos(x) = \sin(x)$

$\displaystyle \frac{d}{dx} \sin(x) = \cos(x)$

$\displaystyle \quad \quad \leftarrow \cos(x) \leftarrow$

$\displaystyle -\sin(x) \quad \quad \quad \sin(x)$

$\displaystyle \quad \quad \rightarrow -\cos(x)\rightarrow $

q = sym.symbols('q')

print(sym.diff(sym.cos(q)))
print(sym.diff(sym.sin(q)))

-sin(q)
cos(q)

f = sym.cos(q)

for i in range(0,4):
    display(Math('\\frac{d}{dx}%s = %s' %(sym.latex(f),sym.latex(sym.diff(f)))))
    f = sym.diff(f)

$\displaystyle \frac{d}{dx}\cos{\left (q \right )} = - \sin{\left (q \right )}$

$\displaystyle \frac{d}{dx}- \sin{\left (q \right )} = - \cos{\left (q \right )}$

$\displaystyle \frac{d}{dx}- \cos{\left (q \right )} = \sin{\left (q \right )}$

$\displaystyle \frac{d}{dx}\sin{\left (q \right )} = \cos{\left (q \right )}$

import sympy.plotting.plot as symplot

f = sym.cos(q)

for i in range(0,4):
    if i ==0:
        p = symplot(f,show=False,label=sym.latex(f),line_color=(i/5,i/3,i/5))
    else:
        p.extend(symplot(f,show=False,label=sym.latex(f),line_color=(i/5,i/3,i/5)))
        
    f = sym.diff(f)
    
p.legend = True
p.xlim = [-3,3]
p.show()