Quotient rule

Quotient rule

To find the derivative of a function resulted from the quotient of two distinct functions, we need to use the Quotient Rule. In this section, we will learn how to apply the Quotient Rule, with additional applications of the Chain Rule. We will also recognize that the memory trick for the Quotient Rule is a simple variation of the one we used for the Product Rule ("d.o.o.d").

Lessons


formula of quotient rule
  • 1.
    Differentiate: y=4x2−x+1x3+5y = \frac{{4{x^2} - x + 1}}{{{x^3} + 5}}
  • 2.
    Differentiate: y=(3−2x9x+1)5y = {\left( {\frac{{3 - 2x}}{{9x + 1}}} \right)^5}
Do better in math today
Get Started Now
2.
Differentiation
2.1
Definition of derivative
2.2
Estimating derivatives from a table
2.3
Power rule
2.4
Slope and equation of tangent line
2.5
Chain rule
2.6
Derivative of trigonometric functions
2.7
Derivative of exponential functions
2.8
Product rule
2.9
Quotient rule
2.10
Implicit differentiation
2.11
Derivative of inverse trigonometric functions
2.12
Derivative of logarithmic functions
2.13
Higher order derivatives
Calculus 1
Don't just watch, practice makes perfect