# 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 l
l = 6 * m * sp.asinh(3 * m) - 2 * sp.sqrt(1 + 9 * m**2)  # Define the function l(m)

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

# 5th: Simplify the derivative (optional step for clarity)
l_derivative_simplified = sp.simplify(l_derivative)

# 6th: Display the result
print("The derivative of l with respect to m is:")
sp.pprint(l_derivative_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 d
d = sp.asinh(4 * x)  # Define the function d(x) = asinh(4x)

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

# 5th: Simplify and display the result
d_derivative_simplified = sp.simplify(d_derivative)

# 6th: Display the result
print("The derivative of d with respect to x is:")
sp.pprint(d_derivative_simplified)  # Pretty print the derivative

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

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

# 3rd: Define the function m
m = sp.atanh(sp.sqrt(g))  # Define m(g) = atanh(sqrt(g))

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

# 5th: Display the result
print("The derivative of m with respect to g is:")
sp.pprint(m_derivative)  # Pretty print the derivative

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

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

# 3rd: Define the function m
m = sp.atanh(sp.sqrt(g))  # Define m(g) = atanh(sqrt(g))

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

# 5th: Display the result
print("The derivative of m with respect to g is:")
sp.pprint(m_derivative)  # Pretty print the derivative

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

# 2nd: Define the variable and the function
x = sp.symbols('x')  # Define 'x' as a symbolic variable
y = -8 * sp.acoth(21 * x**3)  # Define y = -8 * acoth(21 * x^3)

# 3rd: Calculate the derivative of y with respect to x
y_derivative = sp.diff(y, x)  # Find the derivative of y with respect to x

# 4th: Display the result
print("The derivative of y with respect to x is:")
sp.pprint(y_derivative)  # Pretty print the derivative