Ln Definition and 183 Threads

Can anybody recommend a good site to bone up on differentiating and integrating ln and e functions?

f(x)=x^3lnx^2 product rule y'=u'v+v'u u=x^3 u'=3x^2 v=lnx^2 v'=2lnx^2 f'(x)=3x^2(lnx^2)+2x^3lnx^2) but answer in book is f'(x)=3x^2(lnx^2)+2x^2 What am i doing wrong?

Can someone explain how the integration of 1/x = ln x I understand the usual way results in division by zero and that the derivative of ln x = 1/x So my question is, how is the quantity of area under the curve from 1 to x relate to the natural log of x

I am not sure how would I work this problem. Any help would be appreciated. Estimate ln 1. 5 = Integral from 1 to 1.5 dt/t using the approximation 1 2 [Lf (P) + Uf (P)] with P = {1 =8/8, 9/8, 10/8, 11/8, 12/8=1.5}

Ok really dumb one here for you but for the life of me i can't remember. first e^(2lnx) is that equal to x^2 like i said brain fart thanks for the help guys

Homework Statement Differentiate: f(x) = e^(x^3) Homework Equations The Attempt at a Solution lnf(x) = ln(e) + 3ln(x) 1 / f(x) f'(x) = 1 + 3x^2 / x^3 f'(x) = ( e^(x^3) * 3X^2 ) / x^3 However, my book says the answer is 3x^2*e^(x^3). Any help would be greatly...

the intergral of 1/3x either equals 1/3 ln 3x or 1/3 ln x - i don't know which one is correct though because can't you take the 1/3 out of the intergral and then you get 1/3 ln x - so confused - i should really know this...

Homework Statement ln ln ln x^3 Homework Equations The Attempt at a Solution My teacher was going over the review for the final and this was one of the questions. He said the answer is 1/ln ln x^3 but I don't know how to get that...can someone please help me...thank you!

Homework Statement Find the derivative of 1 / ln x Homework Equations N/A The Attempt at a Solution y = 1/lnx First Attempt: y' = -1/x/(lnx)^2 y' = -1 / x(lnx)^2 Second Attempt: ln y = ln (1 / lnx) ln y = ln 1 - ln x...

This is a small part of a bigger problem, but the part I am having trouble with is finding the derivative of... ln[sqrt(x^2+y^2)] I'm sure it is something simple and I remember learning it in Calc I or II but I forgot. Please help remind me! Thank you!

I have some stupid trouble with a simple integration. f(x)=ln(x^(1/2))/x I try using u substitution. u=ln(x^(1/2)) Then du=1/(x^(1/2)*1/(2x^(1/2))dx=dx/(2x) Then dx should be 2xdu Then plugging back in I should have intg(2u*du) which would give me (ln(x^(1/2))^2; yet the answer my calculator...

I'm struggling taking the derivatives of anything with ln or e in it. For example the question y=xlnx/e^x,i have the solution and the first step they have is lny=lnx+ln(lnx)-lne^x. I understand what to do until the last part why is the e^x on top now? If anyone has the time to help me figure...

Please, how can I solve this? ∫ cos x ln x dx I get this: ln x sin x - ∫sin x/x dx but how do I continue from here? Thanks in advance...

I was wondering if anyone could help me with a question I was trying to work through today in our A-level math class. Homework Statement a. Sketch the graph of y= ln(3x) b. The normal to the curve at Point Q, with x coordinate q, passes through the origin. Find the equation of the...

So the problem says "Taking ln10=2.30 estimate ln10.3 using differentials." The only thing I thought of doing was to set an integral from 1 to 10.3 with 1/x being the equation I integrate, but I'm not sure if that is right. Any help?

i need to write a program that sets up a table displaying values of n, sqrt n and ln n from n = 0 - nmax. I've prompted the user to enter a value for integer nmax. but then I've no idea how to make this apply for the value for nmax for my table. this is what i have so far //Problem...

Ok, so it's been a while since I've had to integrate anything, much less something like this. \int \frac{1}{n(1 + \ln{n})^{2/3}} dn I'm thinking u substition for ln(n) and then du becomes 1/n? But, since the ln(n) is in the denominator of a fraction raised to a power, wouldn't that mess...

ln (x+1) = x-3 i know ln is log base e so the equation becomes: e^(x-3) = x + 1 and i can rearrange using algebra to get: e^x = e^3(x+1) but now I am stuck...how can i separate the x's to solve for it? thanks.

In ?LON, OM bisects LN.* What conclusion can we draw from this? a. angle L is congruent to angle N b. LM is congruent to MN C. LO is congruent to ON I think it's B, because OM bisects LN & that's what's left. i need a lot more help, if anyone is interested in helping me IM me at xstarrlit.

The question is to compute the derivative of ln (7x+1)^1/2 (3X^2+x)^5 (x^2-3)^3 e^2x the ln is for both the numerator and denominator I tried the chain rule and came up with this 1 (7x+1)^1/2 (3x^2+x)^5 (x^2-3)^3 e^2x...

may i know from ln(1-x) how to become - [infinity (sum) k=1] x^k / k ? pls help

When you intergrate a Ln ax problem does is the answer always 1/x for example integrate ln 2x does it equal 1/x or ln 3x and so on For some reason when i work it out on paper or my calculator it comes out to 1/x and I just don't think its right. I think I am just being catious since...

I've had troubled sleep because of this...:cry: I tryed a lot and got this... Can you spot any mistakes or give me hints on how to approach this Thanks

The question is: for a Gaussian distribution what is the mathematical relationship between the FWHM and the standard deviation. The equations I'm using are: N(x) =\frac {\ a}{2} N(x) = Ae^- \frac {\ (x-x_2)^2}{2 sigma^2} I equated the equations and started to solve for x. I know you...

I hate it when people prounce ln as "lawn" It's bad enough writing ln instead of log, but pronouncing it ln is just too far.

What is LN? (Example problem requested) What is LN in math, and how do you solve the LN of something?

Whats the difference between log and ln?

How to solve this? ln ( ln ( ln ((e^x) +4)))=e

lim as x->infinity [e^x + x] ^(1/x) Can anyone help me on this please, thanks.

Hey there, I'm trying to work out all the solutions of z for ln(z)=-1. I let -1=ln|z| so then I took exponentials of both sides so I had e^(-1)=|z| so 1/e would equal z. I wasn't sure about having z also equal to -1/e, because since ln(z) = ln|z| + iarg(z) then for z=-1/e then the arg (z)...

Integrat Ln[x]dx!

Summations and calculus gives me fits so please verify my results on these 2 issues: 1. Z = summation ( exp ( - B*E(s)) ) where the sum is over s d/dB of ln(Z) = d/dB (ln (exp(-BEo) + exp(-BE1) + ... exp(-BEn)) = (exp(-BEo) + exp(-BE1) + ... exp(-BEn))^-1 + (-E0*exp(-BEo)...

Hi all. For any of you who have done differential calculus, I need a little help with a problem involving natural logarithms. The question asks to differentiate y = ln x from first principles . It says "use the definition of the Euler number, namely e = lim(n->inf.) (1+1/n)^n.". First...