Love how excited you get when you solve a problem. Awesome.

Note that you can also find solutions where u + v + w ≠ 6, so the premise is wrong. (Example: just replace ⁶√6 with ¹²√36.) The question should be something like: “Find u, v, w with u + v + w =6 such that ...”.

One of my favorite videos of yours; the excitement building as you approach the solution and the flash when it becomes clear 10/10 would watch again

Hi Prime Newtons, I gave this question a try. I did show that u+v+w=6. But my working had a slight variation. Whereas you took the negative sign into the csc(6x), from "-csc(6x)" to csc(-6x)" ( which is also ok because csc is an odd function). I took the negative sign in the square root. Just like 4^(-1/2) = (-2)th root of 4, so is 6(-1/6) = (-6)th root of 6. Both methods prove u+v+w=6, only values of u and v change in each method. Just wanted to point this out. Appreciate your work!👍

Very nice problem and nice presentation. This is one of your best videos. Thank you!

You are a great mathematician .Keep it up !!!

Very nice solution. It looked slightly baffling at first...but following through the differentation steps it become clearer where it was leading. Nice trick to spot that the minus sign could go inside the csc function.

NOTE that we can make sure that u = -6,however ,we could just find that w^(1/v) = 6^(1/6).for example there is a solution that w=36 and v = 12. in this condition u+v+w = 42

I got to the top level of high school maths in Scotland, and did 1st year maths as an under grad at uni. I never encountered cosecent, cotangent, etc, until I went on youtube. It feels like a whole part of maths was just left out.

Easy problem. As always, you did a great job in solving it!

Amazing stuff

Definitely required the biblical pasy after getting 666 at the end of the solution! Jokes aside, love the vids and your enthusiasm!

Thanks for your great content! Keep it up. Like your very pedagogic explanations @ perfect speed!

Looked pretty weird to me at first, but I got it. f(x) = ln cot(3x)/ln6 f'(x) = 1/cot(3x) * -csc^2(3x) * 3 / ln6 = -1/sin^2(3x) * sin(3x)/cos(3x) * 3/ln6 = -3/ln6 * 1/sin(3x)cos(3x) = -3/ln6 * 1/(1/2)sin(6x) = csc(6x)/ (-1/6*ln6) = csc(6x) / (ln6^(-1/6)) = csc(6x)/ -6th root(ln6) 6 - 6 + 6 = 6 Not sure how you properly rewrite negative fractional powers, but that seems about right

It was beautiful the derivative can be simplified very easily

Check check check!!!! Love that.

Excellent explanation Sir. Thanks 👍

Thanks man. Love your vids, and that you use a blackboard like when I was in school!

What a amazing exercise!!!!

beautiful

Hi sir ❤❤ First

I got 73/6. u=6, v=6, w=1/6. Instead of putting the negative sign inside cosec(6x), I put it inside the ln function.

Easy !!!

So satsfine❤❤

Csc(x)/(ln(1/6)^(1/6)) if put negative on bottom instead of top sums to 4/3

What will be the inverse function of f(x) = xe^x?? Someone slove please🙏🏻🙏🏻🙏🏻.

You win the race 😮

why is w omega

AMEN TO THAT

Can i get the source forr this question?

Do you have any online courses?

noice

The problem can have more than 1 solution it is not necessarily the case that u and v and w have to be just 6 or -6.

666 and so this problem has summoned the demon here

Love the math, could do without the evangelism.

a) u + v + w = - 6 + 6m + 6ᵐ // u = -6, v = 6m, w = 6ᵐ b) u + v + w = 6 + 6m + (1/6)ᵐ // u = 6, v = 6m, w = (1/6)ᵐ 𝒇'(x) = csc(-6x)/𝒍𝒏(⁶√6) = csc(-6x)/𝒍𝒏(⁶ᵐ√(6ᵐ) = = csc(+6x)/𝒍𝒏(⁶√(1/6)) = csc(6x)/𝒍𝒏(⁶ᵐ√((1/6)ᵐ), m∈ℕ