Planetarion Forums

'|'empest · 25 May 2003, 20:54

find dy/dx of ln(1+tan^2 x)

How does one go about solving this?

Proteus · 25 May 2003, 21:01

Differential of ln(something) is ( 1/(something) x (differential of something)) I think.

I can't remember what the differential of tan^2 is though. tan^2 sec^2 sounds familiar however.

If it is (and don't take my word for it), the answer would be ((tan^2 x)(sec^2 x)) / (1 + (tan^2 x)).

However, (1 + tan^2 x) is (sec^2 x) I think, which would make the whole thing (tan^2 x).

Don't believe me though, I'm a Classicist!

NEWSBOT3 · 25 May 2003, 21:03

paging Mrl_Jakiri to thread 164612
paging Sarina_Joy to thread 164612

MrL_JaKiri · 25 May 2003, 21:04

Very easily.

Proteus is right you know. (1/something) * d (something) / dx.

Ps. 1 + tan^2 = sec^2.

Proteus · 25 May 2003, 21:05

Quote:

Originally posted by MrL_JaKiri
Very easily.

Proteus is right you know. (1/something) * d (something) / dx.

Ps. 1 + tan^2 = sec^2.

I am? That's amazing! I thought I'd forgotten Maths.

W · 25 May 2003, 21:05

Quote:

Originally posted by '|'empest
find dy/dx of ln(1+tan^2 x)

How does one go about solving this?

First of all, I am unsure on the notation tan^2 x, but will assume it means (tan(x))^2 (which I write as tan(x)^2, call me a coder)
also, I write dy/dx of f(x) as f(x)'

ln(u(x))'=u'(x)/u(x)
u(x)=1+tan(x)^2=sec(x)^2
u'(x)=2tan(x)*sec(x)^2

ln(1+tan(x)^2)'=2tan(x)sec(x)^2/sec(x)^2=2tan(x)

'|'empest · 25 May 2003, 21:13

Danke.

I knew it was a composite function, and that it would be 1/x * dy/dx of tan^2 x, but didn't have an effing clue what that was.

Anu · 25 May 2003, 21:37

int(ln(1+tan(x)^2)*dx)

Help me on this one please

W · 25 May 2003, 21:42

Quote:

Originally posted by Anu
int(ln(1+tan(x)^2)*dx)

Help me on this one please

No?

Anu · 25 May 2003, 21:42

please, pretty please!

Nodrog · 25 May 2003, 21:46

Quote:

Originally posted by Anu
int(ln(1+tan(x)^2)*dx)

Help me on this one please

I solved it in a truly remarkable way, but unfortunately this post is too small to contain the solution.

Anu · 25 May 2003, 21:48

Quote:

Originally posted by Nodrog
I solved it in a truly remarkable way, but unfortunately this post is too small to contain the solution.

Maple is ghey

meaple too?

Proteus · 25 May 2003, 21:50

Quote:

Originally posted by Anu
Maple is ghey

meaple too?

Eh?

Ragnarak · 25 May 2003, 21:51

Quote:

Originally posted by Anu
int(ln(1+tan(x)^2)*dx)

Help me on this one please

do what W did in reverse

int (f(x)'/f(x)) = ln(f(x))
etc

MrL_JaKiri · 25 May 2003, 21:54

Quote:

Originally posted by Ragnarak
do what W did in reverse

int (f(x)'/f(x)) = ln(f(x))
etc

You could do that if it was the derivative of a function divided by the function, but unfortunately it isn't.

MrL_JaKiri · 25 May 2003, 21:54

ps it's f'(x), at least in England and America.

Ragnarak · 25 May 2003, 21:56

Quote:

Originally posted by MrL_JaKiri
You could do that if it was the derivative of a function divided by the function, but unfortunately it isn't.

oops (i only half read it

)

and erm oops again

nm

MrPeach · 25 May 2003, 23:22

Thankyou for reminding me why I quit maths a few weeks ago I was almost regretting it

MrL_JaKiri · 25 May 2003, 23:35

What, applying a really really simple rule?

Anu · 25 May 2003, 23:41

maths is following rules

Proteus · 25 May 2003, 23:41

Maths is fun.

inf · 25 May 2003, 23:45

Quote:

Originally posted by MrL_JaKiri
ps it's f'(x), at least in England and America.

the dy/dx style notation is also used.

f'(x), f''(x) etc. is the french notation.

W · 25 May 2003, 23:45

It's a whole 'nother ball of wax, and one of the reasons I tired of maths.

MrL_JaKiri · 25 May 2003, 23:46

Quote:

Originally posted by inf
both are used, it's the french notation.

That's no excuse!

inf · 25 May 2003, 23:48

Quote:

Originally posted by MrL_JaKiri
That's no excuse!

I have only studied A-Level Maths, we use the dy/dx style.

Anu · 25 May 2003, 23:51

Physicist tend to use the dot thing don't they?
(one dot above f(x) means the first derivative, two dots means the second, and so on)

MrL_JaKiri · 25 May 2003, 23:56

Quote:

Originally posted by Anu
Physicist tend to use the dot thing don't they?
(one dot above f(x) means the first derivative, two dots means the second, and so on)

f dash x usually.

f double dash etc.

Anu · 26 May 2003, 00:04

Method 4

right. used in dynamics and the like

MrL_JaKiri · 26 May 2003, 00:10

I know what it is, I've used it in mechanics at A-level, just never in physics.

MrPeach · 26 May 2003, 00:15

Quote:

Originally posted by MrL_JaKiri
What, applying a really really simple rule?

Not at all, I could do it... Was just that its boring and pointless

(yes i know this doesn't apply to everyone)

MrL_JaKiri · 26 May 2003, 00:18

It being pointless is independent on the individual.

And it isn't.

MrPeach · 26 May 2003, 00:20

Quote:

Originally posted by MrL_JaKiri
It being pointless is independent on the individual.

And it isn't.

No. Its pointless for me to do... Sorry for my phrasing.

Radical Edward · 26 May 2003, 09:39

you lot conjugate.

Proteus · 26 May 2003, 09:59

Quote:

Originally posted by Radical Edward
you lot conjugate.

No, that would be me.

Fleet_Multiplex · 26 May 2003, 11:06

i hate differentiating with ln

Radical Edward · 26 May 2003, 11:09

Quote:

Originally posted by Fleet_Multiplex
i hate differentiating with ln

you especially.

inf · 26 May 2003, 16:22

Quote:

Originally posted by Anu
Physicist tend to use the dot thing don't they?
(one dot above f(x) means the first derivative, two dots means the second, and so on)

That's the newton style notation, rarely used.

djbass · 26 May 2003, 16:38

Ack!:eek:

Just gives me headaches looking at those formulas. Despite my efforts, I never did find any fun in maths. Especially since I loath to work with unknown variables.

=[DJ Bass]=

MrL_JaKiri · 26 May 2003, 20:20

Yeah, the presence of this + thing scares me too.

Radical Edward · 27 May 2003, 07:50

Quote:

Originally posted by inf
That's the newton style notation, rarely used.

pretty much only used in position velocity and acceleration as far as I know.

Dirac notation > |*>

queball · 29 May 2003, 12:09

Quote:

Originally posted by Radical Edward
pretty much only used in position velocity and acceleration as far as I know.

Dirac notation > |*>

more like |*&rang;

I would like help with this question:
Given that y=x^sinh x, prove that
y d²y/dx² - (dy/dx)² = y²/x

My attempt follows:
take logarithms,
ln y = sinhx ln x
differentiate wrt x,
1/y dy/dx = 1/x sinh x + coshx ln x
differentiate wrt x,
1/y d²y/dx² - 1/y² (dy/dx)² = 1/x cosh x - 1/x² sinh x + 1/x coshx + sinh x ln x
multiply by y²,
y d²y/dx² - (dy/dx)² = y²/x ( 2 cosh x - 1/x sinh x + x sinh x ln x )

The question might be wrong but it's doubtful.

queball · 30 May 2003, 02:36

MrL_JaKiri · 30 May 2003, 05:04

Give me a minute, need to find some paper.

[edit]

Can't find any paper.

Do it tomorrow.

Radical Edward · 30 May 2003, 06:11

Quote:

Originally posted by queball
more like |*&rang;

maybe your keyset is different. all I see instead of your > is a box. what do you see instead of mine?

queball · 30 May 2003, 15:29

Quote:

Originally posted by Radical Edward
maybe your keyset is different. all I see instead of your > is a box. what do you see instead of mine?

The ket part of a Dirac vector thing, it look sjust like on http://mathworld.wolfram.com/DiracNotation.html

Anu · 30 May 2003, 15:48

Did you try using sinh x = 1/2 (e^x - e^-x)

Prolly won't make any difference though.

Radical Edward · 30 May 2003, 15:59

Quote:

Originally posted by queball
The ket part of a Dirac vector thing, it look sjust like on http://mathworld.wolfram.com/DiracNotation.html

ok, so either you were point in at my use of the greater than symbol > or saying that Dirac notation = |*>

Bloomers III · 30 May 2003, 16:07

omg nerd alert!^99

the answer is

2

4mathz