What are the derivatives for log(x) and arctan(x)?

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SUMMARY

The derivatives of the functions log(x) and arctan(x) are essential for finding their Maclaurin series. The derivative of log(x) is 1/x, while the derivative of arctan(x) is 1/(1+x^2). To derive the Maclaurin series for these functions, one must apply the series expansion repeatedly, similar to the approach used for sine and cosine functions. The discussion also clarifies that e^x is not equivalent to xlog(e).

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  • Understanding of Maclaurin series expansion
  • Knowledge of basic calculus, specifically derivatives
  • Familiarity with logarithmic and inverse trigonometric functions
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Homework Statement



find maclauren series for: logx and arctan

Homework Equations



heres the maclauren series:
http://img164.imageshack.us/img164/2792/untitledff7.jpg

The Attempt at a Solution



to solve these, do i need to keep applying the maclauren series formula like i would for sin or cos?

in other words, taking the derivative for logx and arctan, if so, can someone start me out with the derivatives, i don't know them.

also is e^x the same as xlog(e) ?
 
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rcmango said:

Homework Statement



find maclauren series for: logx and arctan

Homework Equations



heres the maclauren series:
http://img164.imageshack.us/img164/2792/untitledff7.jpg

The Attempt at a Solution



to solve these, do i need to keep applying the maclauren series formula like i would for sin or cos?
Yes
in other words, taking the derivative for logx and arctan, if so, can someone start me out with the derivatives, i don't know them.

Well, what do you know. Do you not know the derivative of log(x)?

To calculate the derivative of arctan(x), try letting y=arctan(x) noting that now x=tan(y), and then differentiating both sides wrt x.
also is e^x the same as xlog(e) ?

Erm, no, what makes you think this?
 
Last edited by a moderator:

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