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

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

# 3rd: Define the function d
d = 4**(sp.tan(y))  # Define d = 4^(tan(y))

# 4th: Calculate the derivative of d with respect to y
derivative_d = sp.diff(d, y)  # Find the derivative of d with respect to y

# 5th: Display the result
print("The derivative of d with respect to y is:", derivative_d.simplify())  
# Output the simplified derivative

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

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

# 3rd: Define the function a
a = (sp.exp(3*x) - sp.exp(-3*x))**4  # Define a = (e^(3x) - e^(-3x))^4

# 4th: Calculate the derivative of a with respect to x
derivative_a = sp.diff(a, x)  # Find the derivative of a with respect to x

# 5th: Display the result
print("The derivative of a with respect to x is:", derivative_a.simplify())  
# Output the simplified derivative

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

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

# 3rd: Define the function n
n = x**2 * sp.exp(-2*x)  # Define n = x^2 * e^(-2x)

# 4th: Calculate the derivative of n with respect to x
derivative_n = sp.diff(n, x)  # Find the derivative of n with respect to x

# 5th: Display the result
print("The derivative of n with respect to x is:", derivative_n.simplify())  
# Output the simplified derivative

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

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

# 3rd: Define the function m
m = sp.exp(s) / (s**2 + 1)  # Define m = exp(s) / (s^2 + 1)

# 4th: Calculate the derivative of m with respect to s
derivative_m = sp.diff(m, s)  # Find the derivative of m with respect to s

# 5th: Display the result
print("The derivative of m with respect to s is:", derivative_m.simplify())  
# Output the simplified derivative

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

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

# 3rd: Define the function x
x = 5**(-3*t)  # Define x = 5^(-3t)

# 4th: Calculate the derivative of x with respect to t
derivative_x = sp.diff(x, t)  # Find the derivative of x with respect to t

# 5th: Display the result
print("The derivative of x with respect to t is:", derivative_x)  
# Output the derivative