The Tangent Line and the Derivative (Calculus)

In calculus, you’ll often hear “The derivative is the slope of the tangent line.” But what is a tangent line? The definition is trickier than you might think.

Tangent lines are important because they are the best way to approximate a curve using a line. We can then use the slope of the line as a way to measure the “slope” of the curve.

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Written and Produced by Michael Harrison

Michael Harrison received his BS in math from Caltech, and his MS from the University of Washington where he studied algebraic number theory. After teaching math for a few years, Michael worked in finance both as a developer and a quantitative analyst (quant). He then worked at Google as a software engineer for over 5 years before leaving to found Socratica.

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[mallorysmith]

I love how you went over misconceptions of what a tangent line was first before giving the definition of it. Great video. :-)

[q_q]

Great explanation. Calculus is fun when you actually know what's going on

[sudhakarsiitm]

i love the effort you put to make the audience understand the concept of tangent crystal clear.

[bartlx]

I was going to make a video on the subject myself, until I saw this one... The fact that most definitions just talk about this tangent line touching the curve at 'one' point never really satisfied my hunger when looking at graphs. Great explanation, visuals and presentation pace.

[ElNietoPR]

I want to thank you guys for your amazing videos; they are very well made! I just sent a letter to the UN asking them to ask other nations to subscribe. Hopefully, they'll send a letter to all nations imploring them to subscribe to your channel!

[slackbabo]

I really like how you gave examples and then invited the viewer to try to come up with their own definition for a tangent line first. Hopefully you release some new math videos soon. Keep it up!

[petej]

Thank you so much. The definitions with visuals made the Tangent Line and the Derivative easier to understand and appreciate.

[rafaelrincon]

"If you don't mind, I'd like to on a tangent and touch on an important point." lol

[fluffyrawan]

This is amazing, it made me understand the maths we take at school at a deeper level. Now it makes much more sense to me, thank you!

[sccm]

Great vids. I really hope you don't stop making them. Specially next semester that I'm starting calculus

[fahadfaruqi]

I just want to point out the sound design, I've never seen an educational video pay attention that. It was amazing

[nourkhaled]

iam here from egypt wait for ur videos more than any of the lectures at my faculty of engineering :)

[coniferviveur]

A clear and comprehensive explanation enhanced with an extraordinarily good use of graphics.

[rajeshchandrasekharan]

Sir, your class is far above excellent.

[benjidamenji]

greatest teacher I've encountered on YouTube. thank you so much

[jessicaaaaa]

This is so helpful and clear.it really saved me half and hour reading the textbook!

[SuHAibLOL]

I really love calculus and I understand the concepts, but as I teach the concepts to others, I wonder how it can be put best. This is likely the best video I've seen on introducing tangent lines and it was a great watch. Keep it up man!

[OzanYarman]

Squeaky clean explanation with succinct live demonstrations. Perfect teaching method!

[Ihasgun]

I think this is the greatest explanation of a tangent line to a curve I've seen so far

[ahlalkubur]

This is amazing... Best explanation for tangent lines I have watched so far...