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

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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?
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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