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what's the question? which equation is nicest?

What's the goal? Solve for x in this system of equations?

heh, I like the first one ;)

me too! :)

each one is a different question its says compute the derivatives of each function

Oh, OK, are you familiar with (1.) product rule and (2.) quotient rule and the (3.) power rule?

yeah a little

(1.) \[y=e^x*ln(x)\]
(2.) \[y=ln(3x^2)\]
(3.) \[y=\frac{ln(x)}{x^2}+1\]

And you know chain rule? a little, right? ;)

the 1st equation is \[y=e ^{xlnx}\]

yes

yes

Cool, \[y=ln(3*x^2)\] We will use the Chain Rule here

Yes, and to get du/dx we use the power rule

\[x^y = y*x^{y-1}\] is the power rule

Can you finish solving the equation?

ok cause when he explained it in class i did not understand it at all.

All right, how is it now?

ok so for the power rule what do i plug in or do I have to plug anything in

O ok I didn't know whether what I had was right but thats what I just got to.

This maybe the hardest of the bunch because of the substitution, chain rule, and product rule

yea It was

Well, because substitution can be confusing because you introduce a new variable to differentiate on

*or with respect to

O ok

Now (1.)\[y=e^x * lnx\]

Excuse ... me.... are we finding dy/dx or dx/dy?

dy/dx I believe

Thank you. Please continue....

Ok dpflan

*to find

Heh, you're right, man

so callisto when you solved your equation for the second 1 what did you get for your anserw

Thanks, getting a little carried away. Let me step away for a bit

ur doing fine....:)

is the anserw \[y=\ln(3x^2)=1\div 3x^2\]

Not really...
what is \(\frac{d}{dx}lnx\) ?

im not sure

because you can do this many different ways... but in the end, the derivative should be the same...

yes but I was trying to figure out was 2lnx the anserw for #2 or is y=ln(3x^2)=1/3x^2 the anserw

and either way the derivative is the same...

The key point is you need to know what \(\frac{d}{dx}lnx\) is.

Yes, that is a derivative you need to memorize, it will be quite useful

Ok so many of you have said had your own opinion about the equation so which one is the right 1.

Hehe, right, so, what is your opinion? ;p
You can solve a problem many, many, different ways

For you, how would you approach it now that you've seen how we would?

Ok Think the one Callisto gave me is more simple for #2

Definitely, that was an awesome application of intuition

well, and mathematical understanding

ok

May I ask you again- what is d/dx ( lnx) ?

would you multiply it.

Ok is it d/dx(ln(x))=1/x

Yes.
dy/dx = d/dx (ln3 + lnx^2) = d/dx (2lnx) = 2 d/dx(lnx) = ...?

is it 2/x or just 2x Idon't know if its right

Which one do you think? (i) 2/x (ii) 2x

2/x

Yes. That's correct. Any questions?

just 1 when we started simplifying the equation where did you get the 2 from?

\[lnx^a = a\ln x\]

Ok I get it. thanks Callisto

Welcome.