Derivatives of Exponential Functions

[TheSahar58]

For a f(x)= e^-x/(1+e^-x)2, what is equation of tangent line?

[danlinkgan]

Patrick im back at college and im in Calc II, I got an A in Calc I in part thanks to you, I hope I can repeat the miracle again :)

[patrickJMT]

@danlinkgan study hard : ) 

[sharmoota120]

what would you do if you have a^ln(2x) ??????

[azerty1till9]

pie times tea sounds delicious :-)

[iverson92123]

Thanks!

[nxnaruto]

what would y=e^-3x be?



[supahhflychicken]

@nxnaruto -3e^-3x

[letha11egacy]

I'm pretty sure I could answer most of the examples after watching you work it out a few minutes. Then I look at my homework and it doesn't even look similar

[ComputerNerd666]

OMG I DONT EVEN NEED TO GO TO CLASS I CAN LEARN THIS SH"T IN 5 MINS WITH YOU :D

[sokkerking12345]

Hey, what's something like x^x?

[patrickJMT]

@sokkerking12345 that is not an exponential function. you have to use logarithmic differentiation to find the derivative

[PwnagePC]

My math book attempts to explain all of this in just two lines, complicated as hell. You, sir, alleviated my confusion. Thx!

[BostonGreen17]

how about f'(x) of the function: ln[ln(4x^2*sin^2x)]

thank you for the video!!

[altairvrak]

I dont understand a thing...

[pch34O]

@altairvrak

Well, then you're screwed because this is really as understandable as it's gonna get!

[mcovalt]

I love your use of the word "stuff". Such an underrated word.

[titus120]

This is genius!!!

[katerinawsy]

Where can I find an example of how to find the derivative of x to the power of x only a whole lot harder?

[guliseflower]

reallllly u are awsome .. i love u alot :)))

[Altare1994]

Thanks for all the vids. You've helped me to understand every inch of this subject, something my teacher has so far failed to do. In turn you've helped me earn a GPA which has rewarded me with full tuition to any school I want :) Great job!

[patrickJMT]

@Altare1994 ha, sounds like you owe me a nice donation! : )

[danyhighmonster]

can someone reply to me what an "e" stands for like can it be any number or is it a certain type of number please reply i

[VIR092]

@danyhighmonster In official mathematical lingo, e is Euler's number so I would assume in this video it is Euler's number. e = 2.71 roughly. The base of the Napierian logs.

[lakshitaa1]

e is a constant and it's value is 2.71.

it's a certain type of constant, u can't write anything else in it's place

[grandmasternmk]

Thank you for the video.



[patrickJMT]

@grandmasternmk you are very welcome

[suenge]

more harder examples?

[sghayder]

Nice Job!

[lisinka3]

Patrick, can you take derivatives of functions involving absolute values?

[Kickasss119]

thank you for explaining the FULL equation. i was wondering why in the book and in the lecture that when the powers got more complicated that just x, that they tacked on some random shit. Why the hell would they shorten the equation? i think the WHOLE fucking equation is important AT ALL TIMES, they cant just assume that we know this shit

[Pretoriafly]

@Kickasss119: Wow, your comment sure is kick asss. :-B

@patrickJMT: Thanks for your videos. :-)

[JdunnoMEE]

Thank you for this video.. I understand everything. Our professor's so fast in discussing these. Do you have videos like looking for the value of x using this? :)

[DarkDraven7]

I love you..."some complicated stuff" priceless

[5StepsBack]

i am dropping out school now, like seriously youtube have everything i need to learn about math, physics, and etc

[patrickJMT]

@5StepsBack the internet is changing education, that is for sure!

[endauthority]

@patrickJMT its too bad that one cant get credit for learning, but rather time spent in a flawed educational system

[patrickJMT]

@endauthority nothing is perfect. but i would say there are more educational opportunities for people than there ever has been in history, so it is probably not all that bad

[justlikemia3]

my 45 minute calc class summed up in 5 minutes.

THANK YOU

YOU ARE A GOD SEND

[ProfessorRaichu]

OH MY GOD YOUR HANDWRITING IS AMAZING

[DarthMrB]

Just like that top comment says, I see no reason to go to class. My lecturer is terrible and I come back to my dorm confused. Then I start studying here and I understand everything.

[patrickJMT]

@DarthMrB glad my videos help at least :  )

[TheNumber2Pencil546]

man when calc II is all said and done i will have memorized (what seems like) a million formulas/rules/propeties/ident­ities

[pepteamsergi09]

ty



[toxictits]

patricia i love you.

[patrickJMT]

@toxictits my feminine alter ego thanks you

[gregbielak]

Thank you! Really short and to the point on essentially all the types of problems I will encounter in the section of calculus I'm covering right now

[yeahhyeahh]

those adds are so annoying ..one is trying to do their hw and theyre just so distracting ugh

[patrickJMT]

@yeahhyeahh ads are why you get to watch this stuff for free. baby jesus does not pay for this stuff you know. there are plenty of websites where you can pay a subscription and never have to watch an ad if that is what you prefer.

[atlboy72]

Do you know where I can get a good sheet with all the formulas on it from calculus 2?

[patrickJMT]

@atlboy72 well, i suppose it depends on what exactly you are looking for. i am not sure off the top of my head, but if you google 'cheat sheets calculus 2 ' or something like that, you can probably find what you are looking for.

[Ishi1XP]

thank you :")

[charlesbene]

how about e raise to negative x?

[mamu7mich]

you should raise your voice a bit !!

[buhoman3]

What if it's f(x)^x or f(x)^g(x)?

[xlph]

patrickJMT: "I'm so smart I do my math in permanent marker"

Me: "If only..."

[hmlsport]

this guys voice just makes calc so much easier

[Jfrancis221]

Patrick, I'm assuming you have taken physics and most likely did exceptionally well. Therefore, you should start making some physics videos as well!

[sophieroseplatts]

I dont understand, in the proof of why y=a^x when differentiated is a^x x lna

because: take logs of both sides lny = xlna

then differentiate : 1/y x dy/dx = d/dx (xlna) < on this bit how do they differentiate to just lna????

[Muzanywa]

grt wrk...wil hlp m n exam

[Muzanywa]

grt wrk...wil hlp m n exam

[ian559fresno]

awesome videos! Thanks

[rickyrubio94]

every video i see of yours, i get mind fucked....my teacher sucks ass :p

[309401164]

:( you didn't simplify 

[hashmat187]

thank God you're left-handed.

[Morgam06]

Just realized my lecturer is a retard... no actually i think iv known all along.

[dingdingdavid]

nice job, you skip ahead a little, but straightforward and good examples....thanks

[alen132465]

THANK YOU SO MUCH. I take my notes in class very detailed but I still don't understand the concepts 100%. This is like part 2 of my notes and I'm definitely subscribing to you. Thank you and youtube lol

[jackxzx]

where exactly is the bunch of other videos?

[dwarven444]

Your videos are awesome and insanely helpful 

[AnimangaArtist]

Oh my gosh.

I spent 30 minutes trying to teach myself this lesson in my textbook.

I understood it in five minutes, all thanks to you.

You.are.amazing.

[toda9008]

so we'll have e to the stuff times the derivative of the stuff. LMBO if you taught my calc class i would gladly go 2 class cuz my russian prof confuses me :( Your videos are alot of help.

[MisterJesse]

I wish I had found your channel 6 months ago...Your channel is better than all 3 of my different calc teachers on their best days. Rock on dude.

[98hahelos]

with love, from Malaysia. <3

struggling in Australia hahahahaha

[98hahelos]

why dont you have algebra videos? :(

[zhaze420]

i dont even go to class any more i just watch your videos

[patrickJMT]

@zhaze420 ha, go to class

[zhaze420]

@patrickJMT  NO

[wantontrollop]

@patrickJMT

Maths class at 6:30 in the morning does not lend itself to good attendance.

[Skyrodude]

khanacademy = for physics.

patrickjmt = math.

[patrickJMT]

@Skyrodude that is what i want to hear (since all i do is math!) : )

[patrickJMT]

@Skyrodude spread the word

[534coolio]

@patrickJMT Patrick are you a genius at physics too? if you can post some of those it'll be awesome!

[eclipse245]

@Skyrodude too bad physics is easy.... lol Calculus is a destructive Force

[NothingAtAllXD]

@Skyrodude I would have to disagree. Sal Khan gives excellent lectures on both Math and Science areas (and plenty more), but I feel like both patrictJMT and Khan Academy are essential combinations for math success. When I go to these videos, I see interesting things, especially the way each of them approach problems. This is how I get a much more diverse tool chest, I get plenty more tools to choose from. Never ever restrict yourself to one source! Thank you Patrick for this Math Gold Mine here!

[TheHypaLink]

@Skyrodude Not true. Khan definitely goes into Physics, Chemistry and other sciences of course, but he teaches math as good as anyone else.

The difference with Khan and PatrickJMT is that Khan teaches math more intuitively, so you understand WHY you're doing what you're doing. Where as PatrickJMT teaches you how to attack the problems you're likely going to deal with on tests and problems. One's more intuitive, one's more mechanical.

Now watch them both, and you'll become a Super Saiyan.

[cabolisa]

Is it just my computer, or is the volume really low on this vid? I'm having a hard time hearing the audio, and I've got my sound at max volume.  Regardless, thanks for your math vids, they're really helping me in my college algebra class!

[mmykle]

@cabolisa It must just be your computer, I can hear him fine at 34% volume. Try using headphones instead of speakers if your speakers aren't good.

[curlyhair1993]

can you explain why the derivative of f(x)=e^x is f'(x)=e^x please.

im still confused :S

[jenbrenner]

Thanks!  Great video!

[scbaldwin13]

a better wording for the derivative of e^x would be e^x * x' ... that's because if x were 2x, then the derivative would be e^x * 2

[Kingboy676]

thank u very much شكراً جزيلا

[ILOVEGIRLS808]

BYU loves YOU!

[TsukiLune]

I have a question (also test is tomorrow so answer right away would be great) i need to evaluate this: (16 / 9) ^ (2 / 3)  ( ^ means exponent) the answer is 64 / 27 but i have no idea how to get there :(

[patrickJMT]

@Resi2birkin does the order matter?

[patrickJMT]

@Resi2birkin yep

[firenuts1800]

University of Waterloo loves you!

I am sooooo not worried about my calculus midterm tomorrow anymore!

[gengen23100]

YOU ARE AWESOME! Thank you for everything. btw, im a bit confused. whats the derivative of x-e^-x? Is it just 1-e^-x or it is something more complicated. thanks again!

[vplof]

Wow your are the best teacher ever, thank you so much.!!!!!!!

What about x^x^x dont know how to

[tatfr0guy]

@vplof x^(x^x) is kinda crazy. It would help to know the derivitive of x^x first. All you have to do is take the ln of x^x^x=y to get (using the log rules) (x^x)ln(x)=ln(y). then it just becomes an overly convoluted implicit differentiation problem, just take d/dx of bothe side the equation and solve for dy/dx. Hope this helps!

[TheMolo4712]

Thanks!!!! From University of Puerto Rico :)

[AbstractRS]

Patrick, I love you.

[DMoyer91]

can i borrow your brain for my test tomorrow?

[StoN220]

wow dude i seriously don't need to study for my math test tomorrow. Thank you very much

[Romeowasbleeding1]

I should sue you for making me slap my forehead so much all the time! :D

[iniloy1993]

bro, i love you..no homo

[vidoecommenter1]

He's left handed...what do you expect?

[thestateofdecay]

Thank you! You might just help me pass Calculus II. GA Tech Calculus has totally kicked my butt.

[abombinreverse]

Kahn Academy couldnt wipe your but PatrickJMT!

also, he has terrible handwriting!

[patrickJMT]

@abombinreverse ha, well, he is doing good stuff too for sure : ) glad you like my stuff though!

[ny1fanta]

@patrickJMT I do like ur math better than his, no doubt he is a smart dude

[MattyHild]

@patrickJMT

I think both of you guys are awesome. If i watch both khan academy and your videos on a topic, i seem to have a much better grasp of the concept than if i only listened to one. Plus more examples!

[skrevat]

@patrickJMT i laughed at this comment, ITS MATH WARS!!!

[MistaFranko]

@abombinreverse Yoooo!!

Chilll mann!!!! I am a fan of both guys!

[EdMahoney19]

You and Khan Academy are superior expositors. Both of you cut the slack on college stress. Keep up the good work.

[patrickJMT]

@EdMahoney19 glad you like us both : ) khan seems to be taking over the world while i quietly go about my business!

[natdogrocker]

@patrickJMT your a great teacher but i think the reason he's becoming international is because he is not just focused on math he does other subjects and he is set on expanding. I think the way you explain it is formulaic based which to me is better but for people who struggle in Math they like the intuition he gives and the proofs to answer the question "Why the hell do I need this?" Moreover, he is very informal which is comforting for those who see this as Greek. (pun intended :P)

[QuakinginFEAR]

I think maybe adding some proofs for some of the concepts would be nice, but other than that good show mate.

[adoboholic]

ur teaching style is very straight forward and very easy to understand. i like that. are u teaching at a university?

[mishiiee]

This method doesn't work for finding the derivative of x^x

[like9orphanz]

watching youtube is always the best way to study for a text!

[Volcin]

my hope has been renewed thanks to your video. Thank you Patrick.

[mypinkdollprincess]

Thanks for making these vids! They're truly helpful~(:-

[royce97]

I love you... The problem I need help on for my high school calculus final tomorrow is the first one you cover.

[erisontop]

i appreciate the videos and their varied difficulties. they are the only reason i have any idea about what is going on in my calc. course.

thank you for posting these. really.

[gengen23100]

this video is really helpful. thank you

i have a question, i dont know how to get the derivative of h(z)= z^2(1+e^-z)

[elten400]

nice

[Nargaz]

Isn't the last example with cos the product rule?

[neonsmileee]

@Nargaz no, it's the chain rule because there's only one term. the 2^πt is the angle for cos, making it one term.

[airfreak789854521]

awsome! Gosh I was so lost in my lecture. and I saw your vid and Voila! Thanks!

[whooperpooper86]

patrick, i love you and i want you to be my teacher. marry me and u can teach me math and we can have babies and well live happily ever after until im done with high school

[MsEmm22]

can u plz explain the last problem again ?

i didnt understand how u took the derivative of whats inside the brackets

[OARHEGOS]

So great! Thanks so much!

[ily8992]

omg so helpful!!!!!!!!!! thanks =)

[sfcolombia]

you should be my Calculus teacher!!!

[MrKwanlee]

pretty good lecture nice job

[xilllllix]

Once again, easily explained here than in class or in the book.

[username14657]

he's a number ninja

[sm3116332]

You're so awesome!!! I'm soooo ready for this part of the test now, thanks for make it soooooo easy and breaking it up into basic parts! I love all your videos, thanks for helping us all out, you're definitely saving some academic lives:)

[crazyanton1953]

Thank you man. You are just fantastic and funtastic to...

[karlkarlkarl1234]

This guy must have the biggest package.

[babiappl333]

THANK YOU! this really helped. keep it up, your method is really helpful :)

[amjPeace]

Thanks for the explanations, they are much appreciated!

[TheBitchesNCream]

you are jesus in math form, your beard is comprised of heavenly math equations and your halo of awesome explanation

[Skizzorhands]

@TheBitchesNCream LOL!

[sweet16girl657]

wow, lots of "stuff"

[manny95020]

thank you man youre the best.

[XxTNTxX92]

u are my hero

[godzac]

Does anyone know where I can get info of how to graph the integral of f ' (x) when the graph of f ' (x) is given?

[miinibee]

HAHA, I love how you call the function in the exponent "stuff". To the derivative of that "stuff". idk, it's just funny to me lol

[DatATLGurl770]

thank you so much for posting these videos, they really do help alot.

[rEdsNip]

hey do u have a vid abt integration using exponential functions?

[hangloose1350]

The way my textbook tried to explain this made no sense at all...but the way you explain it makes sense. Thank you so much!

[smcwilly08]

i have a problem, e^cosx+lnx

would that just be e^cosx+lnx by (-sinx + 1/x)

[ge4r1a5ldsayz]

i like your teaching style.... the last problem is tough though....

[patrickJMT]

if i make them all easy, people yell at me : )

[macNdow]

why are you so smart?

[patrickJMT]

10% smart

90% willing to work my ass off

[TheDatsunKing]

@patrickJMT I love that quote. Seriously.

I love what you're doing on here, you're single (and left) handedly saving so many kids, including myself.

I can't thank you enough, honestly. You've helped us all more than you could ever imagine. May I ask what you do for a living/studying in school?

[brosbeenrandom]

@patrickJMT hey man, your good at explaining, you should become a math teacher, BUUUT ne ways,i have a question, for my math hw "complete the statement: the gradient function of y=5^x is always......... than the original function." any ideas?

[walkerwiggins0]

@patrickJMT i like your willing to work vs smart ratio but i believe you have it backwards lol

[aztips]

e to the stuff times the derivative of that stuff...he he he...sweet!!

But no doubt, an excellent video!!

[1a1a2a3a]

do you have any videos on applications?

[RThrisala]

you speak in a language i can understand :D . thank you!!!!

[patrickJMT]

you would have to distribute the e^x, yes, if that is what you are asking

[braskasguardian]

Hey, is it possible to intergrate e^f(x) dx? I've been trying to integrate e^(x^2) but it only seems possible to approximate using Taylor series :?

[patrickJMT]

you can not integrate e^(x^2) in terms of elementary antiderivatives.

u are correct : we use taylor series to approximate

[braskasguardian]

ok, thanks!

[scottturner1994]

Thanks, this really helped a lot! I wish all math was taught like this.

[captaineothan]

I think I'll stick with physics :)

[dirtydeeds2447]

Love you usage of the phrase "complicated stuff".

[svfan]

What if you have something like:

X^(2x)

[patrickJMT]

then you use logarithmic differentiation...

fortunately, i have a few videos on that!

[Longmachao]

thx alot, my exam in a couple hour , and i couln't figure it out by looking at the book, they use the same equation but sum how way more confusing then the way you show in your vid.

[patrickJMT]

glad it helped

[ixhapein]

can i you solve this please..i cant understand this equation..

sec²(1-e^ -x)

please..i'll wait for the answer..

thank you..