Derivatives of ALL trig functions (proofs!)

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Derivatives of ALL trig functions (proofs!)

Рет қаралды 45,318

Күн бұрын

Derivatives of trig functions! We will go over the proofs of the derivatives of all the trigonometric functions. The good news is we just need to use the definition of derivative only one that and that is to prove the derivative of sin(x) is cos(x). Then we can use the power rule, chain rule, and also quotient rule for the other functions.
Hope this video helps! This is for both calculus 1 and calculus 2 students. If you need lots of derivative examples, then check out 100 derivatives: • 100 derivatives (every...
0:00 dear calculus students!
0:09 derivative of sin(x) by the definition
5:46 derivative of cos(x) by the co-identity and the chain rule
9:02 derivative of tan(x) by the quotient rule
11:01 derivative of cot(x) by the quotient rule
14:01 derivative of sec(x)=(cos(x))^-1 by the power and the chain rules
17:45 derivative of csc(x)=(sin(x))^-1 by the power rule and the chain rules
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Пікірлер: 38

@jamiewilson3297 Жыл бұрын

This helped me so much! now instead of trying to remember all of the derivatives I can find them myself if I forget!

@Nylspider 2 жыл бұрын

Honestly these are really good exercises for practicing the limit definition of a derivative

@holyshit922 Жыл бұрын

But he used it only for sine , moreover he didnt explain why limit ((cos(h)-1)/h ,h=0)= 0 so even this derivative is incomplete BTW it is easy to express the derivative of sine using limit (sin(h)/h,h=0) only

@gewdvibes 10 ай бұрын

@@holyshit922he said that proof is out of scope of this video and he also said you can just use your calculator to figure out the proof as h approaches 0

@ErdemtugsC Ай бұрын

@@holyshit922just find your own d/dx cosx

@gatjuatwicteatriek4590 Жыл бұрын

This man qualifies to take all the students in the world. I will not get tired of sharing your videos, they are really helping 100%

@user-wu8yq1rb9t 2 жыл бұрын

I don't care it's easy or hard; because it's still Math and it's matter. Therefore I watch it.

@haseebkahn4811 2 жыл бұрын

13:32 I think we have negative sign in the derivatives because in the complimentary angles, we have a negative sign with x ie. {[Pie/2] -x} and d(-x)/dx= -1.

@vukanimakhathini4904 Жыл бұрын

Thank you for this and all the videos you've done they're really helpful

@swapnilmaurya7767 3 ай бұрын

In calculating of the derivative of sinx we can also use the sin c - sind= 2 cos((c+d)/2)*sin((c-d)/2)

@jaydenlee2310 2 жыл бұрын

Thanks a lot man!!! Keep up this great work!

@user-zt4hf2eu6g 2 жыл бұрын

I love your videos. Btw, when u calculated cotx, by writing it as cosx/sinx, i calculated it by typing it as 1/tanx instead

@b4u50 9 ай бұрын

Your love for mathematics is contagious ❤.

@haseebkahn4811 2 жыл бұрын

Thank you so much, Sir! I had to disable adblocker and log in my account to effectively show my gratitude. 😍😍❤❤

@bprpcalculusbasics 2 жыл бұрын

Thank you. You didn't have to do that but I appreciate it! : )

@user-dq5dd4ty7m 2 жыл бұрын

جزاك الله خيرا

@PriggarGaming Ай бұрын

Why are you holding a pokeball so that when we faint from math you can capture us?

@zankopshtiwan1318 Жыл бұрын

You are one of the best

@haris7541 2 жыл бұрын

Brilliant❤

@calixsnts 2 жыл бұрын

THANK YOU SO MUCHH SIR, YOU HELP ME A LOT ABOUT MY ASSIGNMENT

@llvllx Жыл бұрын

Thank you sir

@bhrek3271 2 жыл бұрын

this is very epic

@dalisabe62 7 ай бұрын

The trouble doesn’t end without having to prove the last steps. lim sin(h)/h as h goes to zero needs proof and using the calculator is not a proof. Likewise the other lim that has the cosine term needs proof as well. Other than that, the methodology of the proof looks good.

@user-wu8yq1rb9t 2 жыл бұрын

When the top of your marker fell down, it remembered me the *Matrix* ; but the *Matrix movie* !

@spaceshipastro 7 ай бұрын

thankkkk u sirr

@lifewithdebathequeenslife1858 2 ай бұрын

Please how does sinH give you cosH 😢, why can't i understand this 😢😢

@foremost6233 Жыл бұрын

I love his pokemon.

@gdlorenzodm5664 Жыл бұрын

derivative of (no “co”)+(trig function) = doesn’t have a minus derivative of “co” + (trig function) = has a minus

@fanamatakecick97 2 жыл бұрын

Doesn’t Chen Lu take place no matter what, technically? d/dx (x) = 1, it would be d/dx (sinx) = cosx * 1, which is just cosx Just food for thought

@carultch 10 ай бұрын

Yes, it's just a trivial case of Mr Chen Lu, since multiplying by 1 is a trivial case that leaves the rest of the expression alone.

@user-od9te5kn6i 9 ай бұрын

Bro ...how i can get the formulas written on your shirt..in pdf form..?

@user-klepikovmd Жыл бұрын

This -1 thing is too confusing. Our calculus teacher taught us to never use it and write arc instead

@lumina_ 10 ай бұрын

there shouldn't be any ambiguity if you write it as (cos(x))^(-1)

@user-klepikovmd 10 ай бұрын

@@lumina_ too complicated

@lumina_ 10 ай бұрын

@@user-klepikovmd how lol, it's just an exponent of -1 clearly written edit: oh wait you're referring to when you write inverse cosine, nevermind. I do agree that arccos(x) is probably better

@thexoxob9448 18 күн бұрын

Inverse trig aside, I think cos²(x) should be cos(cos(x)). You literally can already write cosine squared as cos(x)² or (cos x)². Why make a new notation for something that already has a notation just as simple?