# Maclaurin polynomials problem

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.