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.

If f and g are differentiable, then

Example:

Given that , find f ‘(x)

Solution:

Example:

Given that , find f ‘(x)

Solution:

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Quotient Rule
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.

Khan Academy Presents:
Why the quotient rule is the same thing as the product rule.
Introduction to the derivative of e^{x}, ln x, sin x, cos x, and tan x.