Quotient Rule
The quotient rule is an important concept in calculus used to compute the derivative of the quotient (division) of two functions. If you have two functions, and , the quotient rule helps you find the derivative of their quotient
with respect to . Mathematically, the quotient rule states that:
where is the derivative of with respect to , is the derivative of with respect to , and is the derivative of with respect to .
Examples
Example: Find the derivative of the quotient function with respect to .
- Define the functions and :
- Compute the derivatives:
- Apply the quotient rule:
In Sympy this looks like:
import sympy
x = sympy.symbols("x")
u_x = x**2 + 1
v_x = 3 * x - 4
u_prime = sympy.diff(u_x, x)
v_prime = sympy.diff(v_x, x)
w_prime = (u_prime * v_x - u_x * v_prime) / v_x**2
sympy.simplify(w_prime)
Tags: Mathematics