Use implicit differentiation to find the equation of the tangent line at a point (KristaKingMath)

Learn how to use implicit differentiation to calculate the equation of the tangent to the curve at a specific point. Use implicit differentiation to find the first derivative of y, or y', or y prime, then plug the given point into the first derivative to get the slope of the tangent line, m. Plug the slope and the given point into the point-slope formula for the equation of the line, and simplify to get the equation of the tangent line to the curve at that point.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[ryank]

This was really helpful. Now I'm feeling better about my quiz tomorrow. I like the way you break down every step and explain everything you do. I wish you were my calc teacher! Thanks!

[alexiscampbell]

Thank you so much, this video from 10 years ago made the most sense out of all of the videos I watched! I really appreciate this video and how clearly you explained everything.

[rtgaming]

I was really having difficulty solving for y' and compared to the other videos I watched, you were the only one who explained that part so concisely. Thanks so much

[zachpoulsen]

youre an absolute god at explaining and your voice makes me feel confident that i will understand your videos. never stop.

[JazmineJazzyJaz]

Thank you so much! I literally was just bawling my eyes out because I felt like no matter how hard i tried i could never understand calc and after watching a few of your videos i actually UNDERSTAND! I am beyond grateful for these videos and your great way of teaching!

[wigglermain]

you're the polar opposite of my calc teacher in the best way possible!! awesome and helpful video :)

[Elwebon]

You are the MAN! I'm currently an art major taking calculus courses and this video comes as a blessing from the sky! You ma'am - rule over all the tutorials I have come across so far.

[Gibbs]

I seriously cannot thank you enough!!! This is my 3rd video I've watched by you and you have cleared up weeks of confusion in half a lecture period. thank you thank you thank you!!!!

[chrisdvorak]

Thank you so much for laying out the steps in the very beginning of the video. I only needed the first 30 seconds

[kristakingmath]

Yes I do! :) Just type integralcalc along with the topic you want in the search and they should come up.

[roseh]

oh, my gosh - the absolute best teacher I've found on the web!!!

[kristakingmath]

Hey! Currently I'm not doing tutoring... sorry about that! I hope my videos will continue to be helpful to you... Good luck with all of the math classes this semester and next!! :D

[kristakingmath]

I'm so glad you like my teaching style! :)

[kelseyavachua]

Thank you :) The lecture's clearer than our instructors' lecture. It help a lot.

[kristakingmath]

Thanks Keith! You're so sweet! :D Yes, you could have skipped solving for y', and just plugged in (0, 1/2) as soon as you had the derivative equation. Good luck on your test today... you'll do great!! :D

[kristakingmath]

I'm glad I can help! Hope your test went well! :)

[kristakingmath]

Sorry, I'll try to speak more slowly and clearly! :)

[LDuncansix]

you outlined the steps AND THE WHY'S before you started, then re-confirmed the steps and the why's between each one.  I now get it! Thanks.

[martyboyyy]

You just saved my butt in this calculus class. Thank you so much!

[ShortCliperz]

This video is great! you made it so simple and straight to the point. Thanks very much for making this easy, and thanks for all that you do to help students succeed.