derivative of ln(1+1/x), two ways

derivative of ln(1+1/x), two ways,
calculus 1 derivative example,
how to take the derivative,
logarithmic derivative,

blackpenredpen,
math for fun,

[nikhilbhiwandkar]

Hey blackpenredpen
I have a 3rd way to do this
y=ln(1+1/x)
Rasing both the side by e
e^y=e^ln(1+1/x)
e^y=1+1/x ……………(1)
Differentiating wrt x
e^y(dy/dx)= -1/x^2
Dividing both the side by e^y
dy/dx= -1/x^2(e^y)
dy/dx= -1/x^2(1+1/x) [from (1)]
dy/dx= -1/x^2+x
Q.E.D
I hope you will like it

[nicotandotrunz]

It's good that both were mentioned. the Second approach could be more useful in harder equations

[Arthurcoco]

I like the second method by far, if you find yourself with a much more difficult expression the second method is more helpful because you can split the inside in 2 differents functions to derivate which is simpler.

[Nieznany]

First one: pretty straightforward. Second one: nice idea, wish it worked more often

[XESolar]

I really love your channel so much! Thank you for your work

[anatomania]

I like how one method gives you a rational expression and the other method gives you its partial fraction decomposition

[MIsterremix]

Not sure if you still take commenter submitted challenges, but I'd love to see you find the exact value of I know of two ways to do it; one is simple and uses an angle sum formula, the other is really convoluted and uses the law of cosines. I was asked to solve it on Reddit and ended up solving it the hard way, having forgotten the simple way. I'd love to see your take on solving it.

[sss-oldl]

How do you find the integral from 0 to infinity of sin(x^2)/x dx ? I've been stuck on this for a while...

[mihaiciorobitca]

you make a vid about the 1/x devative using the definition ?
i can't find a solution :(

[bruzzel]

Can you do the integral from 0 to 1 of log(1-x)/x dx? No idea how it works.

[na-hgch]

coyld smone help me out with this?
derivative of y= ln(1/1+x)
wrt x
would be appreciable, thanks!

[AndDiracisHisProphet]

there are a lot of things that don't really matter in this video.

[RafaxDRufus]

Easy videos are ok, but we just did this derivative in the previous video xD

[eltapa]

Can you explain what is l'hopital rule? I mean, i know that you derivate the function, but what that mean?

[benjamingiribonimonteiro]

For me, the approach don't really matter