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Whizzies

Member

Registered: 2014-07-18

Posts: 53

Derivative of Ln(x)

I had to find the derivative of 3^log (x^3).

In my study book:

g^log(x) = ln(x)/ln(g) = 1/ln(g) * ln(x) = (1/ln(g)) * (1/x) = 1 / (x ln(g)

Well! I understand most of it but I do not understand this.

1 / ln(g) = 1 / ln(g)

In my head:
Ln(g) = 1 /g

1/ln (g) = 1/(1/g) = g

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Derivative of Ln(x)

Hm, it's all mixed up. How is 1/ln(g) * ln(x) = (1/ln(g)) * (1/x) ?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

Hm, it's all mixed up. How is 1/ln(g) * ln(x) = (1/ln(g)) * (1/x) ?

That is my question. What I wrote there comes straight out of the book. What I say about (what I think) is what I think...

It is supposed to be the proof that f(x) = g^log(x) = dy/dx =g^log(x) = 1/(x ln(g)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Derivative of Ln(x)

Is there any way you could post a picture of that or maybe use LaTeX?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

This one is bothering me

it should be just g. The derivative.

Last edited by Whizzies (2014-08-01 06:44:44)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Derivative of Ln(x)

hi Whizzies,

I'm assuming that's a log base 'e'.

So

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

http://imgur.com/5CDcty0

here is a link;

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

hi Whizzies,

I'm assuming that's a log base 'e'.

So

Bob

I understand what you are doing, but I can't seem to integrate it with my problem (:

I posted a link, so that it is clear for everybody to see, bec I am quite new with latex.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Derivative of Ln(x)

Your image shows the derivative for ln(x) (natural log base e) and also how to differentiate when the log base is different (say, base g)

You can convert another log base like this:

Take logs in base e

Now you can differentiate using the standard method:

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Derivative of Ln(x)

Advice: do not trust any book with all your life

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

Your image shows the derivative for ln(x) (natural log base e) and also how to differentiate when the log base is different (say, base g)

You can convert another log base like this:

Take logs in base e

Now you can differentiate using the standard method:

Bob

Heyyy,

we learn that

= f'
I don't know if people that go to ''normal'' schools also learn it in the

fashion, but I am in a school that compresses 5 years of math in 1 year and I don't really have any basis. I can differentiate and use certain things, but I don't know the real basis (:

The two examples that you portrayed I understand those two.

What my problem is:

http://imgur.com/5H7Gnzv

it says that the derivative of the left side is equal to the right side, but the derivative of

= g. I am sorry I am overthinking this problem and I get stuck

Just now I was thinking what if I differentiated

the answer

.. SO I am doing something wrong, but I don't know what!

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

Advice: do not trust any book with all your life

Good advice ! I learned it a year ago, though! That is why I am asked it, but it seems that I don't undestand something else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Derivative of Ln(x)

the derivative of

Not so.  There are two things wrong here:

(1)  g is a fixed number, not a variable.  So you could replace with k:

and when multiplied by a function of x

(2)  But there's another thing here.

Let's suppose that g is a variable so that

You cannot just invert both expressions to get

After all, you know that

but

And I've just noticed a third thing:

is not the same as

Bob

ps Why have I used dy/dx rather than f' ?

Simply that I don't know how to get a dash when using Latex.  I'm sure that someone will delight in telling me this, now I've admitted my ignorance, so, thanks in anticipation.

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

the derivative of

Not so.  There are two things wrong here:

(1)  g is a fixed number, not a variable.  So you could replace with k:

and when multiplied by a function of x

(2)  But there's another thing here.

Let's suppose that g is a variable so that

You cannot just invert both expressions to get

After all, you know that

but

And I've just noticed a third thing:

is not the same as

Bob

ps Why have I used dy/dx rather than f' ?

Simply that I don't know how to get a dash when using Latex.  I'm sure that someone will delight in telling me this, now I've admitted my ignorance, so, thanks in anticipation.

I am sorry Bob Bundy, but I still don't understand. What is the difference between a fixed number and a variable? So the mistake I make is that I approach the fractal as a variable?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Derivative of Ln(x)

hi

In the equation

3, 2 and 7 are fixed numbers (constants) and x is the variable.

In the equation

it is not so clear because you would expect to have a choice about the value of every letter here.  Nevertheless we still regard a, b and c as being fixed in this sense:

if we talk about the graph, the variable is x.  And if we differentiate, we only regard x as a variable thus

This distinction between letters used as constants and letters used as variables makes a difference as to how we treat the problem.

Suppose you are told that

a = f(x) also, so the equation becomes

If you were asked to differentiate this, you would get

In your log question, g isn't a function of x, so when you differentiate the expression, you have to regard g as a constant.  This means that ln(g) is also constant.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

I had a major DÔH moment this morning. I read you previous post and was like... okay... At first it was hard to understand for me, but when I woke up this morning the dôh came.

I did not apply the product rule! (Dunno if it is the same in English as in Dutch and fixed numbers we call a constante) Thank you!

so the proper derivative is:

f(x)=

f'(x)=

but the ln(x) * 0 = 0

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Derivative of Ln(x)

hi Whizzies,

'Product rule' is good in English.  I would have used 'constant' , but I chose 'fixed number' as I thought it would be easier to understand.  That's my doh moment. 

In all the books I've seen teaching logs, the log base is shown as a subscript, thus:

I'm glad this has become clear for you. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Whizzies

Member

Registered: 2014-07-18

Posts: 53

Re: Derivative of Ln(x)

hi Whizzies,

'Product rule' is good in English.  I would have used 'constant' , but I chose 'fixed number' as I thought it would be easier to understand.  That's my doh moment. 

In all the books I've seen teaching logs, the log base is shown as a subscript, thus:

I'm glad this has become clear for you. 

Bob

Hé Bob,

Yes

this is for the USA and perhaps other countries, but in the Netherlands we use

without the dot. I just remembered that there is a small difference in the notation (:

Well things turned out okay! Im really happy for all the help (: I still have lots and lots of questions (:

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Derivative of Ln(x)

You are welcome.  Post again:

“Help will always be given at MIF to those who ask for it”

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob