# 1st: Import the sympy module
import sympy as sp  # Import SymPy for symbolic mathematics

# 2nd: Define the variable
b = sp.symbols('b')  # Define 'b' as a symbolic variable

# 3rd: Define the function g(b)
g = sp.sec(b) / (1 + b)  # g(b) = sec(b) / (1 + b)

# 4th: Calculate the derivative of g with respect to b
dg_db = sp.diff(g, b)  # Compute dg/db

# 5th: Display the results using pretty printing
print("Function g(b):")
sp.pprint(g, use_unicode=True)

print("\nDerivative dg/db:")
sp.pprint(dg_db, use_unicode=True)

# 1st: Import the sympy module
import sympy as sp  # Import SymPy for symbolic mathematics

# 2nd: Define the symbolic variable
d = sp.symbols('d')  # Define 'd' as a symbolic variable

# 3rd: Define the function c(d)
c = sp.sec(2 * d)**3  # Define c(d) = sec(2d)^3

# 4th: Compute the derivative of c(d) with respect to d
dc_dd = sp.diff(c, d)  # Calculate dc/dd

# 5th: Display the function and its derivative using pretty printing
print("Function c(d):")
sp.pprint(c, use_unicode=True)

print("\nDerivative dc/dd:")
sp.pprint(dc_dd, use_unicode=True)

# 1st: Import the sympy module
import sympy as sp  # Import SymPy for symbolic mathematics

# 2nd: Define the symbolic variable
x = sp.symbols('x')  # Define 'x' as a symbolic variable

# 3rd: Define the function b(x)
b = sp.csc(sp.sqrt(4*x - 3))  # Define b(x) = csc(sqrt(4x - 3))

# 4th: Compute the derivative of b(x) with respect to x
db_dx = sp.diff(b, x)  # Calculate db/dx

# 5th: Display the function and its derivative using pretty printing
print("Function b(x):")
sp.pprint(b, use_unicode=True)

print("\nDerivative db/dx:")
sp.pprint(db_dx, use_unicode=True)

# 1st: Import the sympy module
import sympy as sp  # Import SymPy for symbolic mathematics

# 2nd: Define the symbolic variable
n = sp.symbols('n')  # Define 'n' as a symbolic variable

# 3rd: Define the function t(n)
t = sp.sec(3*n) - sp.tan(3*n)  # Define t(n) = sec(3n) - tan(3n)

# 4th: Compute the derivative of t(n) with respect to n
dt_dn = sp.diff(t, n)  # Calculate dt/dn

# 5th: Display the function and its derivative using pretty printing
print("Function t(n):")
sp.pprint(t, use_unicode=True)

print("\nDerivative dt/dn:")
sp.pprint(dt_dn, use_unicode=True)

# 1st: Import the sympy module
import sympy as sp  # Import SymPy for symbolic mathematics

# 2nd: Define the symbolic variable
t = sp.symbols('t')  # Define 't' as a symbolic variable

# 3rd: Define the function x(t)
x = sp.cos(4*t)  # Define x(t) = cos(4t)

# 4th: Compute the derivative of x(t) with respect to t
dx_dt = sp.diff(x, t)  # Calculate dx/dt

# 5th: Display the function and its derivative using pretty printing
print("Function x(t):")
sp.pprint(x, use_unicode=True)

print("\nDerivative dx/dt:")
sp.pprint(dx_dt, use_unicode=True)