100 derivatives (everything you have to know for your calculus class)

100 derivatives for your Calculus 1 class. You'll master all the derivatives and differentiation rules, including the power rule, product rule, quotient rule, chain rule, and more. We'll also cover implicit differentiation, logarithmic differentiation, and finding second derivatives. Plus, we'll dive into derivatives of all trigonometric and hyperbolic functions, as well as their inverses. Of course, we will also have the definition of the derivative. #calculus #100derivatives #blackpenredpen #math #apcalculus

Check out my other "100-everything" series:

0:00 100 calculus derivatives
Big thanks to Mark Vinci for the time stamps:
Q1, 3:51, d/dx ax^+bx+c
Q2, 5:18, d/dx sinx/(1+cosx)
Q3, 8:31, d/dx (1+cosx)/sinx
Q4, 11:21, d/dx sqrt(3x+1)
Q5, 13:19, d/dx sin^3(x)+sin(x^3)
Q6, 16:48, d/dx 1/x^4
Q7, 18:53, d/dx (1+cotx)^3
Q8, 21:03, d/dx x^2(2x^3+1)^10
Q9, 28:39, d/dx x/(x^2+1)^2
Q10, 34:37, d/dx 20/(1+5e^-2x)
Q11, 38:10, d/dx sqrt(e^x)+e^sqrt(x)
Q12, 41:27, d/dx sec^3(2x)
Q13, 43:57, d/dx 1/2 (secx)(tanx) + 1/2 ln(secx + tanx)
Q14, 52:31, d/dx (xe^x)/(1+e^x)
Q15, 56:26, d/dx (e^4x)(cos(x/2))
Q16, 1:00:05, d/dx 1/4th root(x^3 - 2)
Q17, 1:04:04, d/dx arctan(sqrt(x^2-1))
Q18, 1:07:31, d/dx (lnx)/x^3
Q19, 1:10:25, d/dx x^x
Q20, 1:14:46, dy/dx for x^3+y^3=6xy
Q21, 1:21:35, dy/dx for ysiny = xsinx
Q22, 1:24:22, dy/dx for ln(x/y) = e^(xy^3)
Q23, 1:30:45, dy/dx for x=sec(y)
Q24, 1:35:59, dy/dx for (x-y)^2 = sinx + siny
Q25, 1:40:16, dy/dx for x^y = y^x
Q26, 1:46:31, dy/dx for arctan(x^2y) = x+y^3
Q27, 1:54:43, dy/dx for x^2/(x^2-y^2) = 3y
Q28, 1:58:03, dy/dx for e^(x/y) = x + y^2
Q29, 2:03:46, dy/dx for (x^2 + y^2 – 1)^3 = y
Q30, 2:06:51, d^2y/dx^2 for 9x^2 + y^2 = 9
Q31, 2:17:01, d^2/dx^2(1/9 sec(3x))
Q32, 2:21:35, d^2/dx^2 (x+1)/sqrt(x)
Q33, 2:26:33, d^2/dx^2 arcsin(x^2)
Q34, 2:32:04, d^2/dx^2 1/(1+cosx)
Q35, 2:36:57, d^2/dx^2 (x)arctan(x)
Q36, 2:39:49, d^2/dx^2 x^4 lnx
Q37, 2:42:34, d^2/dx^2 e^(-x^2)
Q38, 2:45:02, d^2/dx^2 cos(lnx)
Q39, 2:47:44, d^2/dx^2 ln(cosx)
Q40, 2:48:52, d/dx sqrt(1-x^2) + (x)(arcsinx)
Q41, 2:51:48, d/dx (x)sqrt(4-x^2)
Q42, 2:54:34, d/dx sqrt(x^2-1)/x
Q43, 2:56:34, d/dx x/sqrt(x^2-1)
Q44, 2:59:03, d/dx cos(arcsinx)
Q45, 2:59:56, d/dx ln(x^2 + 3x + 5)
Q46, 3:01:24, d/dx (arctan(4x))^2
Q47, 3:03:35, d/dx cubert(x^2)
Q48, 3:04:50, d/dx sin(sqrt(x) lnx)
Q49, 3:07:56, d/dx csc(x^2)
Q50, 3:08:50, d/dx (x^2-1)/lnx
Q51, 3:11:16, d/dx 10^x
Q52, 3:13:08, d/dx cubert(x+(lnx)^2)
Q53, 3:17:07, d/dx x^(3/4) – 2x^(1/4)
Q54, 3:19:54, d/dx log(base 2, (x sqrt(1+x^2))
Q55, 3:26:39, d/dx (x-1)/(x^2-x+1)
Q56, 3:29:28, d/dx 1/3 cos^3x – cosx
Q57, 3:32:08, d/dx e^(xcosx)
Q58, 3:33:55, d/dx (x-sqrt(x))(x+sqrt(x))
Q59, 3:34:40, d/dx arccot(1/x)
Q60, 3:37:50, d/dx (x)(arctanx) – ln(sqrt(x^2+1))
Q61, 3:42:22, d/dx (x)(sqrt(1-x^2))/2 + (arcsinx)/2
Q62, 3:47:30, d/dx (sinx-cosx)(sinx+cosx)
Q63, 3:52:45, d/dx 4x^2(2x^3 – 5x^2)
Q64, 3:55:06, d/dx (sqrtx)(4-x^2)
Q65, 3:57:27, d/dx sqrt((1+x)/(1-x))
Q66, 4:01:40, d/dx sin(sinx)
Q67, 4:03:00, d/dx (1+e^2x)/(1-e^2x)
Q68, 4:06:18, d/dx [x/(1+lnx)]
Q69, 4:08:19, d/dx x^(x/lnx)
Q70, 4:10:04, d/dx ln[sqrt((x^2-1)/(x^2+1))]
Q71, 4:13:43, d/dx arctan(2x+3)
Q72, 4:15:55, d/dx cot^4(2x)
Q73, 4:17:47, d/dx (x^2)/(1+1/x)
Q74, 4:20:44, d/dx e^(x/(1+x^2))
Q75, 4:23:13, d/dx (arcsinx)^3
Q76, 4:24:42, d/dx 1/2 sec^2(x) – ln(secx)
Q77, 4:27:08, d/dx ln(ln(lnx)))
Q78, 4:28:51, d/dx pi^3
Q79, 4:34:04, d/dx ln[x+sqrt(1+x^2)]
Q80, 4:37:52, d/dx arcsinh(x)
Q81, 4:46:55, d/dx e^x sinhx
Q82, 4:48:38, d/dx sech(1/x)
Q83, 4:52:51, d/dx cosh(lnx))
Q84, 4:56:21, d/dx ln(coshx)
Q85, 4:57:36, d/dx sinhx/(1+coshx)
Q86, 5:00:35, d/dx arctanh(cosx)
Q87, 5:03:54, d/dx (x)(arctanhx)+ln(sqrt(1-x^2))
Q88, 5:07:23, d/dx arcsinh(tanx)
Q89, 5:10:39, d/dx arcsin(tanhx)
Q90, 5:12:32, d/dx (tanhx)/(1-x^2)
Q91, 5:14:58, d/dx x^3, definition of derivative
Q92, 5:20:41, d/dx sqrt(3x+1), definition of derivative
Q93, 5:26:16, d/dx 1/(2x+5), definition of derivative
Q94, 5:31:18, d/dx 1/x^2, definition of derivative
Q95, 5:35:34, d/dx sinx, definition of derivative
Q96, 5:44:06, d/dx secx, definition of derivative
Q97, 5:54:41, d/dx arcsinx, definition of derivative
Q98, 6:13:26, d/dx arctanx, definition of derivative
Q99, 6:18:35, d/dx f(x)g(x), definition of derivative
Q100, d/dx f(x)/g(x), definition of derivative
Q101, d/dx tetration of x (i.e. x^x^x)

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[VibingMath]

Thank you very much for your effort bprp! This video is also valuable for high school/college level. Sure I will share this with my students! Time stamp as below for those needed:

100 Derivatives
Q1, 3:51, d/dx ax^+bx+c
Q2, 5:18, d/dx sinx/(1+cosx)
Q3, 8:31, d/dx (1+cosx)/sinx
Q4, 11:21, d/dx sqrt(3x+1)
Q5, 13:19, d/dx sin^3(x)+sin(x^3)
Q6, 16:48, d/dx 1/x^4
Q7, 18:53, d/dx (1+cotx)^3
Q8, 21:03, d/dx x^2(2x^3+1)^10
Q9, 28:39, d/dx x/(x^2+1)^2
Q10, 34:37, d/dx 20/(1+5e^-2x)
Q11, 38:10, d/dx sqrt(e^x)+e^sqrt(x)
Q12, 41:27, d/dx sec^3(2x)
Q13, 43:57, d/dx 1/2 (secx)(tanx) + 1/2 ln(secx + tanx)
Q14, 52:31, d/dx (xe^x)/(1+e^x)
Q15, 56:26, d/dx (e^4x)(cos(x/2))
Q16, 1:00:05, d/dx 1/4th root(x^3 - 2)
Q17, 1:04:04, d/dx arctan(sqrt(x^2-1))
Q18, 1:07:31, d/dx (lnx)/x^3
Q19, 1:10:25, d/dx x^x
Q20, 1:14:46, find dy/dx for x^3+y^3=6xy
Q21, 1:21:35, find dy/dx for ysiny = xsinx
Q22, 1:24:22, find dy/dx for ln(x/y) = e^(xy^3)
Q23, 1:30:45, find dy/dx for x=sec(y)
Q24, 1:35:59, find dy/dx for (x-y)^2 = sinx + siny
Q25, 1:40:16, find dy/dx for x^y = y^x
Q26, 1:46:31, find dy/dx for arctan(x^2y) = x+y^3
Q27, 1:54:43, find dy/dx for x^2/(x^2-y^2) = 3y
Q28, 1:58:03, find dy/dx for e^(x/y) = x + y^2
Q29, 2:03:46, find dy/dx for (x^2 + y^2 – 1)^3 = y
Q30, 2:06:51, find d^2y/dx^2 for 9x^2 + y^2 = 9
Q31, 2:17:01, d^2/dx^2(1/9 sec(3x))
Q32, 2:21:35, d^2/dx^2 (x+1)/sqrt(x)
Q33, 2:26:33, d^2/dx^2 arcsin(x^2)
Q34, 2:32:04, d^2/dx^2 1/(1+cosx)
Q35, 2:36:57, d^2/dx^2 (x)arctan(x)
Q36, 2:39:49, d^2/dx^2 x^4 lnx
Q37, 2:42:34, d^2/dx^2 e^(-x^2)
Q38, 2:45:02, d^2/dx^2 cos(lnx)
Q39, 2:47:44, d^2/dx^2 ln(cosx)
Q40, 2:48:52, d/dx sqrt(1-x^2) + (x)(arcsinx)
Q41, 2:51:48, d/dx (x)sqrt(4-x^2)
Q42, 2:54:34, d/dx sqrt(x^2-1)/x
Q43, 2:56:34, d/dx x/sqrt(x^2-1)
Q44, 2:59:03, d/dx cos(arcsinx)
Q45, 2:59:56, d/dx ln(x^2 + 3x + 5)
Q46, 3:01:24, d/dx (arctan(4x))^2
Q47, 3:03:35, d/dx cubert(x^2)
Q48, 3:04:50, d/dx sin(sqrt(x) lnx)
Q49, 3:07:56, d/dx csc(x^2)
Q50, 3:08:50, d/dx (x^2-1)/lnx
Q51, 3:11:16, d/dx 10^x
Q52, 3:13:08, d/dx cubert(x+(lnx)^2)
Q53, 3:17:07, d/dx x^(3/4) – 2x^(1/4)
Q54, 3:19:54, d/dx log(base 2, (x sqrt(1+x^2))
Q55, 3:26:39, d/dx (x-1)/(x^2-x+1)
Q56, 3:29:28, d/dx 1/3 cos^3x – cosx
Q57, 3:32:08, d/dx e^(xcosx)
Q58, 3:33:55, d/dx (x-sqrt(x))(x+sqrt(x))
Q59, 3:34:40, d/dx arccot(1/x)
Q60, 3:37:50, d/dx (x)(arctanx) – ln(sqrt(x^2+1))
Q61, 3:42:22, d/dx (x)(sqrt(1-x^2))/2 + (arcsinx)/2
Q62, 3:47:30, d/dx (sinx-cosx)(sinx+cosx)
Q63, 3:52:45, d/dx 4x^2(2x^3 – 5x^2)
Q64, 3:55:06, d/dx (sqrtx)(4-x^2)
Q65, 3:57:27, d/dx sqrt((1+x)/(1-x))
Q66, 4:01:40, d/dx sin(sinx)
Q67, 4:03:00, d/dx (1+e^2x)/(1-e^2x)
Q68, 4:06:18, d/dx [x/(1+lnx)]
Q69, 4:08:19, d/dx x^(x/lnx)
Q70, 4:10:04, d/dx ln[sqrt((x^2-1)/(x^2+1))]
Q71, 4:13:43, d/dx arctan(2x+3)
Q72, 4:15:55, d/dx cot^4(2x)
Q73, 4:17:47, d/dx (x^2)/(1+1/x)
Q74, 4:20:44, d/dx e^(x/(1+x^2))
Q75, 4:23:13, d/dx (arcsinx)^3
Q76, 4:24:42, d/dx 1/2 sec^2(x) – ln(secx)
Q77, 4:27:08, d/dx ln(ln(lnx)))
Q78, 4:28:51, d/dx pi^3
Q79, 4:34:04, d/dx ln[x+sqrt(1+x^2)]
Q80, 4:37:52, d/dx arcsinh(x)
Q81, 4:46:55, d/dx e^x sinhx
Q82, 4:48:38, d/dx sech(1/x)
Q83, 4:52:51, d/dx cosh(lnx))
Q84, 4:56:21, d/dx ln(coshx)
Q85, 4:57:36, d/dx sinhx/(1+coshx)
Q86, 5:00:35, d/dx arctanh(cosx)
Q87, 5:03:54, d/dx
Q88, 5:07:23, d/dx arcsinh(tanx)
Q89, 5:10:39, d/dx arcsin(tanhx)
Q90, 5:12:32, d/dx (tanhx)/(1-x^2)
Q91, 5:14:58, d/dx x^3, definition of derivative
Q92, 5:20:41, d/dx sqrt(3x+1), definition of derivative
Q93, 5:26:16, d/dx 1/(2x+5), definition of derivative
Q94, 5:31:18, d/dx 1/x^2, definition of derivative
Q95, 5:35:34, d/dx sinx, definition of derivative
Q96, 5:44:06, d/dx secx, definition of derivative
Q97, 5:54:41, d/dx arcsinx, definition of derivative
Q98, 6:13:26, d/dx arctanx, definition of derivative
Q99, 6:18:35, d/dx f(x)g(x), definition of derivative
Q100, 6:24:57, d/dx f(x)/g(x), definition of derivative
Q101, 6:33:44, d/dx tetration of x (i.e. x^x^x)


YAY!

[rekiplay]

i'm more surpised by the fact that he has been holding that microphone for almost 7 hours stright

[nutmaster]

I don’t even do math or calculus or whatever but seeing this dude so passionate about teaching kids just made my day. we need more teachers like him (:

[tanviranzum]

Watch it backwards to learn integrals!!

[yasinmalik]

I became expert in derivative calculus after solving continuous 100 problems a lot of respect from the bottom of my heart.I wish I could like your video more than 1 time.

[blue-iuhv]

All of you educational youtubers are honestly the backbone of online learning this pandemic 😭😭 thanks a lot!

[chase]

This is clear evidence that we are not all built the same

[emirulusoy]

I prepared for the summer school final of my Calculus course, which I failed in the fall semester, with this video and your integral starter video. And I passed the exam! Thank you very much for your hard work

[frankpoveromo]

There was 0 shot I watched this whole video but I appreciate you. This was a very honest and sincere thank you at the beginning of the video and I think you seem like a very good teacher. This is what the world and education especially needs, and that's more people like you.

[spiderjerusalem]

"Fear no man who does 100 derivatives, but a man who does 1 derivative for 100 times" ~ bruce lee

[janda]

100 integrals, 100 series, 100 trinomials and now 100 derivatives? Bro, the time and effort put into this, I give you the maximum respect I am cabable of

[Acaerwen]

Encountered this video while studying for my calculus exam. I already had my exam 4 days ago and never in my life would I think at 2 am, bored, looking for a thing to do, I'd say "Maybe I'll go back to the 100 derivatives video and do some derivatives". Honestly, you made this fun and a very rewarding learning experience. I couldn't believe and still can't that you would actually do this in ONE video! Thank you so much for doing this. This really helped me hammer in the needed practice, understanding and usage of derivative rules. I only wish I found this video earlier so I could have had such a strong basis of derivatives from the get-go :O

I will definitely be watching more videos and learning from them.

[anshulkumarsingh]

Love that how he smiles while catching his breath every single time he rubs the whiteboard, also little jokes here and there just to make sure we don't doze took the time to write out ALL steps+explanations, i can relate to the sigh of relief after each full sheet of derivatives is completed because i have been following him throughout this period with drinks by my side. The fact that he only takes a 3 MINUTE break in between this madness shows his commitment to help us. Excellently-executed session with everything covered about basic derivatives all while maintaining a positive mindset(though we can feel his internal pain and mentally-drained energy as well as the gigantic muscle cramp of his left arm). Moments like intentionally solving them the wrong way gives us a better understanding on the dos and donts of derivatives. Feels really satisfying after this session because i don't need to worry about STPM calculus for the most part ( that is until i am greeted by the "other" family right after this). (Will definitely come back for 100 integrals and differential equations later on). Keep up the good work because you teach WELL, looking forward to your future videos. Remember! Your efforts are NOT unnoticed.

[thinix]

Teacher: tonight's homework only has 1 question
The one question:

[jarrydhorn]

Imagine if after almost 7 hours he found out that he forgot to start recording.

[josebustamante]

I love how passionate he gets, he really is enjoying this. I hope I too can find something I can be this passionate about to do for the rest of my life

[FlatTopRob]

I recently bought a book called " Pocket Book of Integrals and Mathematical Formulas" by Tallarida and it contains an insane amount of reference information. For some reason I'm fascinated by the idea of familiarizing myself with every equation in the book and writing them out. To my point, you have absolutely motivated me while I continue my journey to get my BS in Mathematics. Thank you!

[alecpena]

Is anyone gonna talk about how he writes with two markers in the same hand and flawlessly transitions between the two?

[seutio]

Hi I'm from Brazil, I'm studying in Brazil, thanks for the wonderful marathon of derivatives, it's been a while since I studied this subject, the way you presented it was perfect, and I don't understand English, except for some basic words, so that's the way you explained it, it was so that anyone who wants to learn can understand even if they don't know english, congratulations.

[michaeledwardharris]

Man, I studied the heck out of this video. This was truly excellent! Teacher quality 10/10.