Calculus – Quotient Rule
In these lessons, we shall learn to find the derivative using the quotient rule.
Related Pages
Calculus: Derivatives
Calculus: Power Rule
Calculus: Product Rule
Calculus: Chain Rule
Calculus Lessons
Math Worksheets
The quotient rule is used to find the derivative of the division of two functions.
The Quotient Rule
The quotient rule says that the derivative of the quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
The following diagrams show the Quotient Rule used to find the derivative of the division of two functions. Scroll down the page for more examples and solutions on how to use the Quotient Rule.
If f and g are differentiable, then
Example:
Given that 
, find f ‘(x)
Solution:
Example:
Given that 
, find f ‘(x)
Solution:
Why the quotient rule is the same thing as the product rule?
Introduction to the derivative of ex, ln x, sin x, cos x, and tan x.
Calculus: Quotient Rule and Simplifying
The quotient rule is useful when trying to find the derivative of a function that is
divided by another function. As long as both functions have derivatives, the quotient
rule tells us that the final derivative is a specific combination of both of the
original functions and their derivatives.
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