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

  • Thread starter rcmango
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In summary, the conversation is about finding the Maclauren series for log(x) and arctan(x) and whether or not the derivatives need to be applied. The provided Maclauren series can be used for both functions, and the derivatives can be found by using the power rule. It is also clarified that e^x is not the same as xlog(e).
  • #1
rcmango
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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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  • #2
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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FAQ: What are the derivatives for log(x) and arctan(x)?

What is a Maclauren series?

A Maclauren series is a type of mathematical series that represents a function as an infinite sum of polynomials. It is named after the Scottish mathematician Colin Maclauren.

How is a Maclauren series helpful in solving problems?

A Maclauren series can be used to approximate a function with a simpler polynomial expression, making it easier to calculate values and solve problems. It is especially useful in calculus and physics.

What is the general formula for a Maclauren series?

The general formula for a Maclauren series is:f(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...where a is the center of the series.

How do you determine the accuracy of a Maclauren series approximation?

The accuracy of a Maclauren series approximation depends on the number of terms used in the series. The more terms included, the more accurate the approximation will be. However, it is important to note that some functions may require an infinite number of terms for a completely accurate representation.

How can I use a Maclauren series to calculate derivatives?

A Maclauren series can be used to calculate derivatives by taking the derivative of each term in the series. This can simplify the process of finding higher order derivatives, as the coefficients of the series can be easily determined using the power rule.

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