in-class derivative vs derivative on the test!
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- Опубликовано: 25 янв 2022
- Let's talk about how to take the derivative. Of course, I will give you an example of the derivative of sqrt(x) first, then there's a test question, the derivative of sqrt(x)^sqrt(x) for you to try!
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Class: d/dx sqrt(x)
Midterm: d/dx [sqrt(x)^sqrt(x)]
Final:
d/dx [sqrt(x)^sqrt(x)^sqrt(x)^...]
Just differentiate y = exp(-W(-ln(sqrt(x)))) and you're done
If that tower of roots is f(x), f'(x)=f(x)/(x-xln(f(x))
Final question's answer would be:- [sqrt(x)^sqrt(x)^sqrt(x)......]/[x-x(sqrt(x)^sqrt(x)^sqrt(x)....)logx]
The final will be to prove the derivative using first principles and extra points for verification via epsilon delta definition at x=1
0:40 one over tooth power
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You could do logarithmic differentiation for d/dx sqrt(x)^sqrt(x)! I like your method too! This cracked me up haha, love it :)
😂
Logarithmic differentiation is essentially equivaleny
It is maybe more easy to substitute u = \sqrt x
You end up with d/dx (\sqrt(x)^\sqrt(x)) = d/du (u^u) du/dx
And this results in the more clear result: 1/2 u^(u-1) (ln u - 1)
Exam questions be like compared to what's thought in classes pretty much lol!!! Btw did you change your channel bprp?
PS: NVM, holy what??? Congrats you are nearing 1mil subs, damn feels good to see how your channel grew, I am or was a long time watcher back then lol!!!
"a little bit more difficult"
Just a little nothing too crazy
I laughed through the entire video 😂😂
😆
Thank you professor
You are a cool calculus teacher.
Coolest*
@@arniie5288 Right.
I just found out that the chain rule is never going away!
thanks
Nice video. Please can you make a video on how you create your thumbnail
Did he forget to cut the start of the vid? XD .
Nice video i love it just like always
The final question on the test that is worth 50 points will be taking the indefinite integral of e^x^2 dx
Then finish off with a bonus question of calculating to which real value the harmonic series of 1/n converges
Oh let’s not forget the final jeopardy, solving the equation x=x+1
In school we take it equal to y and take log both sides
my teacher I have a question which is mathematiciansn say "any number raised to the power of zero other than zero is always equals to 1." why zero is exception. my teacher in school said to me it is not how many times it was multiplied . what helps me to know how many times have been multiplied, as I know every number multiplied by Zero is Zero.
1:45
yeah they look about the same, I'm just gonna diff the sqrt(x) first so we have 1/2sqrt(x)
Ok so d/dx y^y=d/dx e^ylny=y^y*(y'lny+y'*y/y)=y^y y' (lny+1)
y=sqrt(x)=> d/dx sqrt(x)^^2=sqrt(x)^^2 *1/(2sqrt(x))((lnx)/2+1)
you cant take the derivative of y in terms of x
use d/dy, not d/dx
@@pranavkondapalli9306 Yes I can take the derivative of y in terms of x, because y is a function of x.
You are right that I could just have differentiated y^y in terms of y and appended y' which would yield the same result.
Can you investigate Integral of (1+tanh x)/(1+tan x) ? Does it have a solution? And how can one decide if the antiderivative of some expression can be found?
well, try solving it using integration by parts, let 1+tanhx be u and 1/1+tanx be v
∫uv dx = u ∫vdx - ∫ u' (∫vdx)
substitute and hopefully find an answer
btw ∫vdx = 1/2(ln(sinx+cosx)) if youre interested :)
Honestly, I would have done this implicitly.
Cool video
How often are introductory calculus classes in college weed out classes that are unnecessarily difficult?
The weed-out classes are typically in universities rather than community colleges since university professors generally care more about research rather than teaching.
d/dx(?) = c, a constant
cx + d, c & d are constants
Actually ur correct n I'm also but forgot to multiple by x^x 🤣🤣🤣
I used another method let y = x^x then take both side log n proceed
Please write in English.
Why can't I just use the rule you applied in the example?
d/dx sqrt(x)^sqrt(x) = sqrt(x) * sqrt(x)^(sqrt(x) - 1) * 1/(2sqrt(x)) = (x^((sqrt(x) - 1)/2))/2
Would this approach be incorrect? Why?
Because the exponent is also a function of x. The 'power rule' is for constant exponent.
Couldn't you just use implicit diff for this? Let y = sqrt x ^ sqrt x, re-arrange to x^(1/2x^1/2), then ln both sides, and diff both sides then multiply by the y at the end?
Maybe he's more familiar with this technique than implicit diff
this is called logarithmic diff, implicit diff is mostly for equations that cannot be expressed as y in terms of x
@@pneujai hahah smart edit, ok I'll delete my comment
Yes this is just the way to do it without setting the whole thing equal to y and taking logs. It’s equivalent.
@@stephenbeck7222 yes exactlyyy
*laughs in implicit differentiation*
needs a little trick. thanka
Please do d/dx(cube root of x^2)
P/S:I like your math videos🥰🥰🥰
cube root of x² is same as x^2/3. Take power out and subtract 1. And you are done.
@@Shreyas_Jaiswal oh thanks
😂😂😂 you know-how students feel
Please don't put this on a test in your calc 1 class
In class:
Here is how to solve the integral of x^2.
Here is how to solve the integral of tan(x)
In test:
How do you solve world hunger?
funny -_-
You lost me after the "e"
I wished this wasn't accurate 🙁
😆
Ur answer is wrong I guess my one come different
Please write in English.