How to Use Quotient Rule?
Quotient Rule is a method in calculus for finding the derivative of a function that is the ratio of two differentiable functions. The quotient rule formula is given below:
d/dx{g(x)/h(x)} = [g(x) × h'(x) – h(x) × g'(x)] / [h(x)]2
d/dx [u(x)/v(x)] = [v(x) × u'(x) – u(x) × v'(x)] / [v(x)]2
where,
- u(x) is the first function which is a differentiable function
- u'(x) is the derivative of function u(x)
- v(x) is the second function which is a differentiable function
- v'(x) is the derivative of the function v(x)
To use Quotient Rule follow the steps added below:
Step 1: Identify the Functions u(x) and v(x)
Step 2: Differentiate u(x) to get u′(x)
Step 3: Differentiate v(x) to get v′(x)
Step 41: Apply the Quotient Rule Formula (as added above)
Step 5: Simplify the Result
Related examples are added below:
How to Use Quotient Rule?
Quotient rule is an important of derivatives. To find the derivatives of complex fractions this quotient rule is used. The quotient rule helps to find the derivative of complex fractions very easily. It is used to find the derivative when the problem is given in fraction form i.e. in the numerator and denominator form.
This article is about the quotient rule in derivatives, and how it is applied and used.
Table of Content
- What is Quotient Rule?
- How to Use Quotient Rule?
- Quotient Rule Examples
- Practice Questions on Quotient Rule
- FAQs on Quotient Rule