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I am having trouble with derivitives. I understand them but once I get to the point where I need to simplify them I get increadibly stuck. For instance, y=xlog(sub2)x all over (1+x). I got it to the point where it is 1+x(log(sub2)x+1/ln2)-xlog(sub2)x all over (1+x)squared then I don't know what to do from there.
Note that log2x = lnx/ln2.
If you are trying to differentiate this, the derivative is
((1+x)(d hi) - xlnx/ln2)/(1+x)^2.
Now the d hi is if f(x) = xlog(sub2)x,
then f'(x) = x(ln(2)/x) + lnx/ln2.
Putting that back in gives
((1+x)(x(ln2/x) + lnx/ln2) - xlnx/ln2)/(1+x)^2.
Multiplying out each term gives
((1+x)ln2 + lnx/ln2 + xlnx/ln2 - xlnx/ln2)/(1+x)^2.
The third and fourth terms cancel, leaving
((1+x)ln2 + lnx/ln2)/(1+x)^2.
This can be split into two terms. They are
ln2/(1+x) + lnx/(ln2(1+x)^2).
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