Solving Complex Log Derivatives: y = log_2(x^2+1)

[iamsmooth]

Homework Statement

$$y = \log_{2}(x^2 + 1)$$

Homework Equations

I think the pattern is:

$$\frac{d}{dx}[\log_{b}(x)] = \frac{1}{x ln(b)}$$

The Attempt at a Solution

$$y\prime = \frac{2x}{(x^2+1)ln(2)}$$

I did this by applying the pattern (that may or may not be correct) and then chain ruling the middle. If this is correct, then would this amount of work be acceptable (as you can kind of eye it without doing much work)?

When we do weird functions like $$y=x^x^2$$ I know how to do them by taking the ln of both sides and playing around with log properties, since this is the only kind of question that came up on quizzes, it's the only kind of log derivatives I'm familiar with.

Anyways, thanks.

 

[Borek]

Quick and dirty approach:

http://www.wolframalpha.com/input/?i=d(log_2(x^2+1))/dx

 

[iamsmooth]

Is there a reason why the denominator log(2) instead of ln(2)?

ln(x) != log(x), no?

Thanks for the webpage, seems awesomely useful for future reference.

 

[Borek]

First line below the derivative states "log(x) is the natural logarithm"...

 

[iamsmooth]

Oh whoops, sorry.

Thanks a lot, appreciate the timely help :D