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

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

# 3rd: Define the function k
k = sp.exp(sp.sqrt(m)) * sp.cosh(m)  # Define k = e^(sqrt(m)) * cosh(m)

# 4th: Compute the derivative of k with respect to m
k_derivative = sp.diff(k, m)  # Find the derivative of k with respect to m

# 5th: Simplify and display the result
k_derivative_simplified = sp.simplify(k_derivative)  # Simplify the derivative
print(k_derivative_simplified)  # 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 t
t = sp.tanh(sp.sqrt(x)) * sp.csch(sp.sqrt(x))  # Define t = tanh(sqrt(x)) * csch(sqrt(x))

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

# 5th: Simplify and display the result
t_derivative_simplified = sp.simplify(t_derivative)  # Simplify the derivative
print(t_derivative_simplified)  # 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 d
d = sp.sinh(2 * s) / (sp.exp(s) - sp.exp(-s))  # Define d = sinh(2s) / (e^s - e^(-s))

# 4th: Differentiate d with respect to s
dd_ds = sp.diff(d, s)  # Find the derivative of d with respect to s

# 5th: Simplify the expression using trigonometric identities
dd_ds_simplified = sp.simplify(sp.trigsimp(dd_ds))  # Apply trig simplifications and simplify

# 6th: Print the derivative in a simple form
print("The derivative of d with respect to s is:")
sp.pprint(dd_ds_simplified)  # Pretty print 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 h
h = sp.log(sp.sech(x))  # Define h = ln(sech(x))

# 4th: Differentiate h with respect to x
dh_dx = sp.diff(h, x)  # Find the derivative of h with respect to x

# 5th: Simplify the derivative
dh_dx_simplified = sp.simplify(dh_dx)  # Simplify the derivative

# 6th: Print the derivative
print("The derivative of h with respect to x is:")
sp.pprint(dh_dx_simplified)  # Pretty print 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 w
w = sp.cosh(x) / sp.exp(x)  # Define w = cosh(x) / exp(x)

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

# 5th: Simplify the derivative
derivative_w_simplified = sp.simplify(derivative_w)  # Simplify the derivative

# 6th: Display the result
print("The derivative of w with respect to x is:", derivative_w_simplified)  
# Print the simplified derivative