How to Find Maclaurin Polynomials for ln(x) in Sigma Notation?

[raincheck]

Homework Statement

Find the Maclaurin polynomials of orders n=0, 1, 2, 3, and 4, and then find the nth Maclaurin polynomials for the function in sigma notation:

f(x)= ln(1+x)

Homework Equations

pn(x)= f(0) + f'(0)x + [f''(0)/2!](x)^2 +[f'''(0)/3!](x)^3 + ... + [f^(n)(0)/n!](x)^n

The Attempt at a Solution

I know that I need to find up to the 4th derivative using f(x)=ln(x) and then simply use the maclaurin polynomial equation up to a certain point for n = 0, 1, 2, 3, 4 .. n.

The only problem is I can't remember how to FIND derivatives of ln(x)!
I don't really understand how to find the nth polynomial in sigma notation either..

Thank you!

 

[Zell2]

What integrates to give ln(x)? (How is it defined?)
The nth polynomial bit will probably become clearer once you've written down a few of the derivatives.

 

[raincheck]

Well, I thought (1/x) integrates to ln(x), but I wasn't sure about the derivative...

 

[Zell2]

So what's the realtionship between integrating and differentiating?

 

[raincheck]

OH okay i just realized at the beginning of the problem i was referring to ln(x+1) and then somehow i changed it to ln(x). i understand about the relationship between ln(x) and 1/x, i just need help with the derivative of ln(x+1)

thank you!

 

[Zell2]

Try letting u=x+1

 

[raincheck]

soo.. ln(u)du =1/(u) ? so its just 1/(x+1) ?

wow, i thought it was a lot harder for some reason.

 

[Zell2]

That's right.