Aunty Em Well-Known Member Dec 14, 2002 #21 I've got a headache! It's at least 6 years since I did that without the aid of a computer.
Luis G <i><b>Problemator</b></i> Staff member Dec 14, 2002 #22 Just for the sake of it.......i remember this problem in one of my high school calculus course Differentiate x^y = y^x Have fun.
Just for the sake of it.......i remember this problem in one of my high school calculus course Differentiate x^y = y^x Have fun.
Luis G <i><b>Problemator</b></i> Staff member Dec 14, 2002 #24 Luis G said: Differentiate x^y = y^x Click to expand... My bet is that SL will do it
F fury Administrator Staff member Dec 14, 2002 #25 Luis G said: Just for the sake of it.......i remember this problem in one of my high school calculus course Differentiate x^y = y^x Have fun. Click to expand... Both x and y are 2
Luis G said: Just for the sake of it.......i remember this problem in one of my high school calculus course Differentiate x^y = y^x Have fun. Click to expand... Both x and y are 2
Luis G <i><b>Problemator</b></i> Staff member Dec 14, 2002 #26 That'd be correct if wasn't asking to differentiate
Luis G <i><b>Problemator</b></i> Staff member Dec 14, 2002 #28 hint y^x = x^y ln(y^x) = ln(x^y) x ln(y) = y ln(x)
Squiggy ThunderDick Dec 14, 2002 #30 I heard that prolonged exposure to this kind of stuff can make you start peeing in the shower.... Well, thats what I heard....
I heard that prolonged exposure to this kind of stuff can make you start peeing in the shower.... Well, thats what I heard....
Jeslek Banned Dec 14, 2002 #31 Luis G said: Just for the sake of it.......i remember this problem in one of my high school calculus course Differentiate x^y = y^x Have fun. Click to expand... Take the ln of both sides: y*ln x = x*ln y y = x*(ln y / ln x) Diff: y' = (ln y / ln x) + x * (dy/dx [ln y / ln x]) y' = (ln y / ln x) + x * ( (1/x)*ln y- (1/y)*ln x) / (ln x)^2
Luis G said: Just for the sake of it.......i remember this problem in one of my high school calculus course Differentiate x^y = y^x Have fun. Click to expand... Take the ln of both sides: y*ln x = x*ln y y = x*(ln y / ln x) Diff: y' = (ln y / ln x) + x * (dy/dx [ln y / ln x]) y' = (ln y / ln x) + x * ( (1/x)*ln y- (1/y)*ln x) / (ln x)^2
Luis G <i><b>Problemator</b></i> Staff member Dec 14, 2002 #32 It is incomplete. You need to express the differentiation in terms of "x", not x and y y' = something expressed in terms of x
It is incomplete. You need to express the differentiation in terms of "x", not x and y y' = something expressed in terms of x
Jeslek Banned Dec 14, 2002 #33 Duh ok, I see... So we have x^y = z and y^x = z, therefore for any non-zero zee, x = y... Let me think about this.
Duh ok, I see... So we have x^y = z and y^x = z, therefore for any non-zero zee, x = y... Let me think about this.
Luis G <i><b>Problemator</b></i> Staff member Dec 14, 2002 #35 i know i did that one before........but it's been ages since my last calculus course. Maybe i'm way far from the answer, but this is so far what i have.
i know i did that one before........but it's been ages since my last calculus course. Maybe i'm way far from the answer, but this is so far what i have.
Shadowfax <b>mod cow</b> Dec 14, 2002 #38 lol, that's what i was thinking o wait, i need to know this for my exams in a few months....nah, i'll improvise
lol, that's what i was thinking o wait, i need to know this for my exams in a few months....nah, i'll improvise
Aunty Em Well-Known Member Dec 14, 2002 #39 Squiggy said: I heard that prolonged exposure to this kind of stuff can make you start peeing in the shower.... Well, thats what I heard.... Click to expand... Oh, so that's why.... and there was me thinking it was just a weak bladder.
Squiggy said: I heard that prolonged exposure to this kind of stuff can make you start peeing in the shower.... Well, thats what I heard.... Click to expand... Oh, so that's why.... and there was me thinking it was just a weak bladder.
