Different Differentiation Rules

Calculus Tutorial

Different Differentiation Rules

Intro

Any problem that can be solved with the quotient rule can also be solved with the product rule and chain rule.

Sample Problem

Find the first derivative of:

f(x)

Solution

Quotient rule:

Separate the numerator and denominator into two separate functions, then find their derivatives.

g(x)
h(x)

g'(x)
h'(x)

Plug into the quotient rule formula:

quotient rule

first step

You can expand the answer if you like, but this is sufficient.

————————————————————-

Now for the Product Rule. This time, we will turn the denominator into a negative exponent:

product rule

g(x) will remain the same, but h(x) and h'(x) will look like this using the chain rule:

h(x)

hprime

And plug into the product rule:

productrule

pluginproductrule

reduce

midstep

first step

You should arrive at the same answer in both cases



About The Author

Math, Computer Science, And Writing Tutor
Hello! My name is Jesson and my tutoring experience extends over 5 years, with several subjects at nearly all levels of education. I have over 3 years experience as mentor for elementary school students (K-5) in after school programs in Oakland and San Francisco, tutoring primarily with English writ...
Send Email
11 Subjects
KnowRo Tutor
5 Tutorials
$50
Vallejo, CA
Learn

Suggested Tutors for Calculus Help

Ad

Varsity Tutors

(855) 475-5132 - Award-Winning Academic & Test Prep Tutors

Ad

Link Educational Institute

Link Educational Institute

Sophia G

Washington, DC

General Tutor

Abdul B

Arlington, VA

Math And Science Expert

Leave a Comment

Your email address will not be published. Required fields are marked *

^