Using Implicit Differentiation to find a Second Derivative

[@emmanuel3929]

What my professor couldn't explain in 3 hours you did it in 6:28 mins. You sir have my respect. Thank you man

[@GenevaRob72]

Your professor needs to pay...dearly.

[@Brisun]

You know life is good when his first example is identical to your homework

[@lowere11]

Sana All

[@jmromero7025]

naol hahah

[@ahymnsa]

Thank you! I'm writing a calculus exam tomorrow and this helped a bunch! I was sitting confused for a whole hour before I found your video. Thanks so much.

[@brianwalker3659]

Thank you so much for this video. Putting the original equation back in finally clicked for me. Once again thanks for making your video so meticulously step by step.

[@one0xin]

2 weeks of this in class...i did not understand a thing and 6 minutes of ur examples....i finally get it!! thank you so much!

[@erikbrowning667]

11 years on KZbin and still the best math lessons online

[@Gunnerz93]

THANK U SO MUUUUUCH AAAAHHHHHHHHH..!! i swear, you are so much better at explaining than any of my lecturers or tutors or anything... i should be paying u!!!!! u are the reason for me passing maths this year :p i will tell all my friends about u!!!!!

[@KeenanJones1]

oh thank god I found this. You and Google just saved my Calculus grade a few percents. You have my undying gratitude.

[@Elusefelier]

You, sir, deserve my thanks. These lessons are extremely clear and have helped me a ton. THANK YOU.

[@setboy1]

Thank you. My teacher didn't show us how to substitute in like that. I had been pulling my hair out trying to figure out how to do this very problem from my book and getting no where and then i came here and found you doing the same problem!!!

[@patrickjmt]

i hope it helps! : )

[@patrickjmt]

happy to help!

[@bigbluewhale99]

Thank you for actually making this make sense!! I will personally thank you in my graduation speech

[@patrickjmt]

Miranda Whalen haha, that would be sweet!

[@greetlesday13]

Thank you so much! My professor was explaining this super complicated-like and it only made sense just now! I'm so glad that I won't lose points on my midterm for this since it's actually so simple!

[@jkristia2011]

Very helpful video. From the text book I was having a hard time understand the substituing dy/dx part, you video made it really obvious. Thank you very much

[@neonorangeflowers]

if i could reach you i would probably hug you right now thank you so much for this video

[@patrickjmt]

i live in austin, tx and very much like hugs

[@neonorangeflowers]

i live in cleveland, ohio :'D my arms are not quite long enough

[@patrickjmt]

@Balkance ha - just me being breathy into the mic

[@xshingie]

*high fives fellow left-hander* You rule! I love how simply/clearly you explain this. My teacher talks at hyperspeed and her processes have gaps in them... Anyway, thank you SO much!

[@theCastielz]

Your last tip at the very end of the video saved my sanity. I kept getting the wrong answers in my textbook and didn't realize why until I watched this! So thank you very much!

[@lkarki100]

This is the same problem that is assigned on Webassign. The person in WebAssign video is making me more difficult to understand while in here the same problem is explained with great depth. Thanks for your help now I can complete my homework.

[@patrickjmt]

Write we assign and tell them to hire me

[@lkarki100]

patrickJMT Here is the link if you are interested in applying. www.webassign.net/

[@brakatsuuu00]

lkarki100 im using webassign too. ill agree with you, if patrickJMT is the person in webassign video i think everyone can perfect that exercises there.

[@brakatsuuu00]

lkarki100 im using webassign too. ill agree with you, if patrickJMT is the person in webassign video i think everyone can perfect that exercises there.

[@VcTrN]

You've taught me more in one video than what my teacher did in three weeks. -,- Thanks. :D

[@my80yearoldman]

OMG that last step where you let y^2 +9x^2 = 1 !!!!

[@crazyrandom3]

Woah. The substitution at the end?? My teacher didn't teach that... That's so interesting! I never even thought to simplify it that way! Thanks! You helped a lot!

[@patrickjmt]

thanks for spreading the word :)

[@imnotgovernorwatts]

you are calculus god uve helped me now in high school calculus and university level calculus thank you

[@AngusTaoHuang]

You are very patient, I love all your video in which you shared with. :)

[@CorySiebler]

Thank you! Figured out the problem once you showed how you insert the first derivative for (dy/dx). Makes so much sense I feel silly for not recognizing it without watching this video!

[@dpreed94]

thanks man! now i'm ready to rock my BC Calculus exam tomorrow!

[@Jackangell7]

Some people were have the natural ability to teach, you have this ability good sir. Not all Hero's wear capes! 😀

[@monsterific5337]

honestly you're a better prof than my calculus prof.

[@ianronson419]

you are literally doing god's work king tysm!!!

[@MustafaAfify97]

Thank you very much now i finally understand after 7 hours of my teacher explaining, respect.

[@MustafaAfify97]

+Christie Lord haha its just a matter of going over and over the same concept then you will eventually get it, good luck.

[@MrRaveLincoln]

Ty Patrick. You saved the day again. Subscribed!

[@quinnjones2886]

Wow, 14 years and still helping calc students to this day :)

[@hasans7370]

Hey Patric! at 2:48 I think you should have distributed the minus sign to both of the variables [(-9x) and (1*-9x/y)] so both of them will have a positive sign, right! Or at least that what I think! Does anyone have a clue? And I just wanted to say you are the best teacher I've ever listen and seen in math. I wish you were my professor lol! Thank you :)

[@Alfalotter]

It is -(-9x)(1*-9x/y), so 3 minuses in the term means minus overall.

[@Casanova0411]

Thank You so much! My teacher screwed up teaching us this in class and basically screwed me and my classmates because the class was over. Nice writing and step-by-step instruction! 4 Stars out of 4 !

[@sebaxh22]

Great video, you explain this way better than my professor. Thanks again, Cheers!

[@11window]

Thankyou for providing me with this for cramming. This stuff isnt that hard makes me wish i went to lectures this semester :)

[@dylancurrier7363]

Thank you! This 10 year old video taught me this better than my teacher.

[@peppercorg]

OH MY GOSH. thank you sooo much. my math teacher didn't really help me, but you did. YAY :D

[@yikuzaian]

Very helpful...THank you.Hope more people see your videos.

[@ZeroTwoRazer]

I believe that PatrickJMT and KhanAcademy are one of the best "teachers/professors" is because that they dont teach use with pedagogy, they both explain it in layman's term so that we would understand. I tried helping my class before by asking the professor to link one of your videos ( would of been wiser to link the channel ) but he said he wasn't able to because there was no pedagogy involved. Sad that we have to learn through one view point rather than other view points.

[@youngzzterwiil27]

You are the reason im not failing ap calc. gracias amigo!

[@mickifree12]

you sir... are a genius, I knew the answer was -81/y^3, but i just didn't know how to go from -9(y^2+9x^2)/y^3, until you pointed out that it was equal to 9 =p

[@GoofyGooberSWAT]

when he divided the whole numerator by y^2 shouldn't he have taken the reciprocal and multiplied it, thus canceling out the Y in the denominator ?? idk I'm probably wrong. around 4:10?

[@genesislayne3322]

You're right

[@mustafamufasa]

@Vikki1331 it actually sounds more confusing the way you state it. looking back i see that the 9*(9x^2 +y^2) looks the same as the starting equation which was equal to 9. so i'm assuming he was able to substitute in right?

[@drewski91]

You have made my life so much easier.

[@claybee12]

10 years later and you come through like the Kool-Aid man 👊🏾, thanks.

[@patrickjmt]

ohhhhhhh yeeeaaaaa!

[@justinhua4085]

who else is getting killed in AP Calculus right now?

[@SweetnPreppy]

I had a quick question. If you have to find the derivative of -3y, would the answer be -3 or -3dy/dx? I'm a little confused. Thank you so much, your videos are the only reason I'm getting an A in AP Calc!

[@TheAnenomeEnemy]

You're a life saver.

[@Syruscleat]

Great presentation. The substitution is a bit mind-blowing.

[@ncousn5137]

seriously man thanks, good job explaining it.

[@tonymoma9647]

Thanks man, this really helped a lot.

[@hajia.9448]

You are the best, MAN!!!

[@vitords]

This helped me a lot! Thank you.

[@jopopzzz]

Pls make more vids about this topic. Theone much harder than this one because in the exams, they don't give this type of problem :)

[@inayatpahuja]

Absolutely beautiful question! Had fun solving it:)

[@patrickjmt]

i *heart* chess

[@moony9327]

could you derive " xsiny=ycosx " for the second derivative using implicit differentiation???

[@vipuldaripkar]

you saved my life. thank you

[@jessicalin129000]

This was really clear thank you!

[@jonahjohnson7230]

New to calc so I'm a novice lol... just wondering if I was to express dy/dx as -9x(y^-1) and use product rule, would that work as well?

[@patrickjmt]

@villex4 y ' = dy/dx

[@haebi-chan]

efing savior! thanks man. gotta ace that quiz tomorrow

[@gellyrosepinkyvillanueva4454]

Thankyou for this video. Help a lot :)

[@ishpreetanand]

Why didn't you take out 9 outside as a constant and then solve for the second derivative ?

[@jpmoench21]

dude!!! you are the man! thanks

[@mustafamufasa]

how were you able to substitute 9 for (y^2+9x^2)

[@StuPip]

@setboy1 It's unfortunate that we have to pay so much money for textbooks that just don't seem to help in situations like this. Thank you very much, PatrickJMT for clearing this up.

[@escarlai]

at 1:50,what the name of the rule you talk about? thank you:)

[@AlvinGinole]

Thank u for ur video. It helped me a lot. Sending a virtual hug 🤗💘

[@Connroy17]

Thank you! my math teacher cant teach for shit, i just watch ur videos and now i have an A in AP Calc

[@bellacarolita]

im confused, you are using dx/dyis equal to y' prime, cause i was tauhgt that every time you make a derivative to y yoou should add y'

[@MsStarwanderer]

Thanks for the help!

[@androcci]

have you ever consider buying Wacom tablet? connecting it to the computer and writing the math problems there? i think it would be awesome if you would do your videos like this!! just saying :P

[@qwertykeyboardqwerty]

how do you record your vids bro? do you like wear a tripod on yer head?

[@jashperjameslechadores8268]

what if, y is bigger than x? how can I divide it? thank you in advance

[@arturosanchez6291]

THANK YOU SO SO SO SO SO SO SO MUCH !

[@mollyc2575]

Amazing math. Second derivative is just amazing. Just on this video perhaps?

[@Tucknrollgrampa]

Really good stuff!

[@Venom22Spiderman]

Awesome, this is the EXACT same problem I need help on for my homework! O.o

[@asdlgvfrbadkhjaseygf]

thanks sooo much u helped me a lot

[@Nile49]

You rule! Thanks a ton!

[@VehnFromDiscord]

Can you show me how to Implicitly Differentiate right handed?

[@ifeojewuyi6495]

U are a god send. thank you!

[@RParamoL]

wow. i really like that last substitution. i was NOT taught that. well. to be honest. im not really getting taught much. :p dude. you're amazing.

[@tanishasethi4441]

thank you for this video!

[@villex4]

I dont get it!!! is y prime equal to dy/dx or dx/dy?

[@168grhp]

so helpful, thank you!

[@DKRaFiQ]

why must the derivative of "y" be dy/dx??

[@nrashu]

Thank you so much! I wish you were my teacher! D':

[@DanikonLUK]

5:48 how does y^2=9 i have no clue

[@emekaukaga]

Thanks so much dude, you cleared a lot of things up for me. :)

[@theopenstack]

.Sir : An case of derivative where we apply Natural log to Both side of equation .? How I will know that here we will apply log to perform dy/DX Pls help .... Thanksss

[@methamphetamememcmeth3422]

If you've got something like a variable raised to a variable.

[@theopenstack]

Is this the case sir.

[@akbarthegreat03]

thanks man...i get it now, i got a test on these today lol

[@ahmedalgadi515]

I don’t understand how the last step works. The step where you replaced (y^2+9x^2) with 9

[@lilbluehersheykiss]

that was beautiful.

[@johnnolen8338]

Using logarithmic differentiation to find the 2nd derivative instead of the quotient rule speeds up the calculation a lot IMHO.

[@trisjafaye653]

Why can't I download it. 😥