Master the essential concepts of differential calculus and develop expertise in analyzing rates of change and solving optimization problems. In this comprehensive course, you'll learn to calculate derivatives from first principles, apply advanced differentiation rules including product, quotient, and chain rules, and use implicit differentiation to handle complex equations with interdependent variables.
Differential Calculus Fundamentals
Gain insight into a topic and learn the fundamentals.
Intermediate level
Recommended experience
1 week to complete
at 10 hours a week
Flexible schedule
Learn at your own pace
What you'll learn
Calculate derivatives from first principles and apply product, quotient, and chain rules to differentiate complex functions systematically.
Use implicit differentiation to handle equations with interdependent variables and compute higher-order derivatives for function analysis.
Identify and interpret maxima, minima, and inflection points using derivative tests to solve optimization problems effectively.
Apply differential calculus techniques to analyze rates of change and model real-world phenomena in data science and engineering contexts.
Skills you'll gain
Details to know
Shareable certificate
Add to your LinkedIn profile
Recently updated!
February 2026
Assessments
8 assignments
Taught in English
See how employees at top companies are mastering in-demand skills
There are 4 modules in this course
This module introduces you to the concept of derivatives, helping you understand how rates of change are represented graphically and calculated from first principles. Through readings and hands-on examples, you will begin applying derivatives to simple functions and real-world scenarios.
What's included
3 videos11 readings2 assignments
This week you will explore the product, quotient, and chain rules to differentiate more complex functions. Applying these rules through guided examples and by solving increasingly challenging problems you will gradually build your confidence.
What's included
2 videos9 readings2 assignments1 plugin
The focus this week will shift to implicit differentiation, where you will learn to handle equations with interdependent variables. Activities include solving higher-order derivatives and applying the technique to practical problems.
What's included
2 videos9 readings2 assignments1 plugin
This module covers maxima, minima, and inflection points, showing you how to identify and interpret them using derivatives. You will apply these concepts to optimization problems and explore their relevance in data-driven decision-making.
What's included
2 videos6 readings2 assignments1 plugin
Instructor
Offered by
Why people choose Coursera for their career
Felipe M.
Learner since 2018
"To be able to take courses at my own pace and rhythm has been an amazing experience. I can learn whenever it fits my schedule and mood."
Jennifer J.
Learner since 2020
"I directly applied the concepts and skills I learned from my courses to an exciting new project at work."
Larry W.
Learner since 2021
"When I need courses on topics that my university doesn't offer, Coursera is one of the best places to go."
Chaitanya A.
"Learning isn't just about being better at your job: it's so much more than that. Coursera allows me to learn without limits."
Open new doors with Coursera Plus
Unlimited access to 10,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription
Advance your career with an online degree
Earn a degree from world-class universities - 100% online
Join over 3,400 global companies that choose Coursera for Business
Upskill your employees to excel in the digital economy
Frequently asked questions
To access the course materials, assignments and to earn a Certificate, you will need to purchase the Certificate experience when you enroll in a course. You can try a Free Trial instead, or apply for Financial Aid. The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile.
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.
More questions
Financial aid available,