Definition of the Derivative

This calculus video tutorial provides a basic introduction into the definition of the derivative formula in the form of a difference quotient with limits. It explains how to find the derivative of a function using the limit process. This video contains plenty of examples and practice problems.

Derivatives - Formula Sheet:

Full-Length Math & Science Videos:

___________________________________
Derivatives - Fast Review:

Limit Definition of the Derivative:

Derivatives - Alternate Limit Definition:

Derivatives - The Constant Rule:

Derivatives - The Power Rule:

_________________________________
Derivatives - Constant Multiple Rule:

Derivatives - Polynomial Functions:

Derivatives - Sine and Cosine:

Derivatives - Trigonometric Functions:

Derivatives - Limits:

_______________________________________
Equation of the Tangent Line:

Derivatives - Horizontal Tangent Line:

The Equation of The Normal Line:

The Equation of The Secant Line:

Average and Instantaneous Velocity:

_______________________________________
Final Exams and Video Playlists:

[tambahsaah]

I have dropped Calculas three times in three semester because after struggling to pass the 40 mark out 100 in all the tests, it was obvious Math was not my thing. This guy has saved my life. I got 48 out of 100 in my first exam for this fall and I considered dropping again until I found this guy. Second exam I got 84 for the first time in my existence on earth in math.🤣 Now I’m like a boss in class answering all the questions 🤣😂

[gilttcn]

Thank you sir .. The only teacher on the earth who is a Mathematician but can't count his students

[spritfun]

From high school to university, his tutorials are always golden! Thanks!

[Bnelen]

I used to think people were joking when they said they learn more from here than school.
Now in Uni I can absolutely confirm. I rely heavily on these tutorials - doesn't help that my school provides nothing but problems to solve.

[JackLetzelter]

Imagine being the sole reason for probably thousands of kids graduating college every single year. You are making a huge impact on this earth and we all really appreciate it

[davidlzda]

I swear down, this guy's voice is literally so soothing.

[myphone]

I just want to hug this man and say thank you. He makes everything so easy to understand.

[Noogai]

This 2 year old video of yours are still saving students like me from poor lecturers. Thank you, you magnificent being. I'll support you fully when I have a job someday and it'll be all thanks to you.

[viprflowrs]

I wouldn’t be able to do the math in my engineering program if it wasn’t for this dude right here. Thank you for being my teacher the past couple of years!

[superbutter]

When a 20 minute video beats ur whole semester of school

[ichangedmynamealotoftimes]

Been watching your videos since I was in 8th grade, now I'm in 11th grade and your videos heavily helped me get through general math, trigonometry, pre-calculus, calculus, and Chemistry! Thank you!

[bruv]

bro i went from literally failing out of math 4, not knowing how to factor, or literally nothing about the unit circle, to an 86 on my limit exam for calc in one summer thanks to you. Absolute fucking legend, I hope to do even better on this derivative exam to prove how good of a resource you are.

[miraculoushulumununum]

It's not even my professors fault i'm flunking, but your videos really do a great deal of help in my studies. I'm really slow when it comes to these kinds of things, so my brain can't process the lessons whenever I attend class. Thanks a bunch! :)

[sanashandholder]

nah but why am i attracted to his voice studying has made me fr delirious 😭

[jordanmuwanguzi]

Best youtube tutor no doubt...which they create awards because usually he deserves them...lots of love 🙄🤞🏿

[ranavantaepurple]

Since I have been watching your videos I believed that my teachers cannot be teachers and the money that I give to them should be given to you because you are the one who simplize everything to me and made me understand very well so a huge thanks for your hard work you helped me so much❤️❤️

[reemmizari]

somebody come pick my jaw up from the floor. This guy is my savior. FINALLY I GET IT! THANK YOU!!

[ldfreak]

Yo you are honestly the reason I am gonna pass calculus this semester. idk how you manage to teach this stuff so much better than my actual professors, but you do! Thank you!

[statik]

I was literally crying over how the actual f*** I get f(x+h) thank you so much, this teaches me way more than in school

[aiyshasulaiman]

Watched like 10 of your videos and they are so helpful! Thank you so much!