derivative of x^(1/x), calculus 1 tutorial

derivative of x^(1/x),
implicit differentiation,
logarithmic differentiation,
calc 1 derivative problem,

math for fun,

[SciHeartJourney]

Thank you for doing every little step and being strict in following the rules of math. This series of videos is excellent!

[AndreMillerRocks]

Tutored calc 1 for 3 years, never once thought to do it the second way. Neat!

[arurak]

U can do by taking once x constant and apply x to power n formula and adding to it by applying to a to power x formula keeping a constant and u get same result

[postholedigger]

Instead of trying to cram to get through a test, this format presents the opportunity to actually learn and understand the material. Now mathematics can be transformed from a competitive memorization exercise into an educational experience.
SEAN

[sansamman]

I have learned so much from you and books and studying at first when I started watching I hated you I was like( this Chinese guy is solving equations for him self, done.)
few months later I came across you again and realised how cool you are.
now I already know what you are going to do next { I'm bonded with you *-* }

[guilhermegondin]

For this function in particular there is a very clever and nice way to do it without implicit differentiation nor logarithmic differentiation:
First set y = ln(x)/x, so by the product rule, y' = (1-ln(x))/x^2.
now, set y = ln(x^(1/x)) (it's the same thing up to algebraic operations), so by the chain rule, y' = 1/x^(1/x) * [x^(1/x)]', wich means that y'*x^(1/x) = [x^(1/x)]'.
but by or first derivative we know that y' = (1-ln(x))/x^2, so [x^(1/x)]' = x^(1/x)*(1-ln(x))/x^2.

btw, am I the only one who says yey! with the kids in the video intro? LoL.

[iabervon]

One of these days, you should do d(x^2)/dx by taking the log. e^(2ln x)d(2ln x)/dx=2e^(2ln x)/x. Like the time I integrated 1/x^2 by trig substitution successfully before realizing that there's an easier way. But you can prove that the power rule works for non-integer constant exponents.

[MrCigarro]

Thank you for this and all of your great videos. They are a great help for me and all of my students. Could you do a video on the meaning of d(f(x)), the differential of a function? Thanks in advance.

[b.namita]

Thank you very much, dear sir
we appreciate your work

[RedIceberg]

You can use the first method to derive a general rule for d/dx(u(x)^v(x)). You end up with f'(x) = f(x) treated as x^b + f(x) treated as a^x. Or, in other terms, f'(x) =

[MrRyanroberson]

(1-lnx)x^(1/x -2) you get the idea for the first solution, more efficient writing.

[Chai_yeah]

Dayum now I am curious to know when will you use it !!

[friedkeenan]

I like just using the general equation for the derivative of f(x)^g(x)

[nhopf]

The second solution seems to be simpler to me! Since d(x^x)/dx was also calculated by implicit differentiation (in a previous video), this is an obvious strategy for those who already were bprp subscribers at the time.

Nice video, by the way! We need some differentiation here!

[UchihaNiteesh]

Thank you very much Sir ❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

[leonardobarrera]

I like mos the first, because the chain rule is very complex, I think that coplex numbers are less complex that the chain rule!!!!

[dcs_]

i remember this from the e^pi vs pi^e video!

[jeromesnail]

I like the right one better. Never been a fan of implicit differentiation anyway ^^

[jimnewton]

Isn't x equal to an exponential only valid when x>0 ? Isn't x=ln( exp(x)) the correct transformation as that's a true equality?

[omerangi]

You should make a video about how important math is, because i think most people don't get that... The most important mathematical proof there is