Hello,
I'm not getting these questions. Could someone please help me out? 
find d/d(x2) [ (a+x2)(1/2)/(a+x2)2 ]
and also this one:
differentiate with respect to x
y= 3* 2x+1
and another one 
:
differentiate:
|(1-3x)/2|
I know it's Christmas, and probs people won't answer but 
thanks
Yeesh - no sleep for the wicked.
I'm going to take this time to remind you all to have regular breaks - nothing wrong with a day or two off! Particularly if you spend months straight studying, it's not healthy, and you'll hurt your brain and be less effective for SACs/exams.
The first one, you could of course apply the quotient rule - but I'm gonna use exponential rules:
^{1/2}}{(a+x^2)^2}<br />\\ =(a+x^2)^{1/2-2}=(a+x^2)^{-3/2})
Now, we want to take the derivative with respect to x^
2, not just x. This can be confusing, so let's make a substitution to make life easier. Let u=x^2:
^{-3/2}\right]<br />\\ =\frac{-3}{2}\left(a+u\right)^{-3/2-1}<br />\\ =\frac{-3}{2}\left(a+x^2\right)^{-5/2})
For the second, we note that we can only differentiate exponentials of base e. That translation is going to be annoying, so I'll get rid of it. You can of course try this yourself without removing the translation:
}=6\cdot e^{x\ln(2)}<br />\\ \frac{dy}{dx}=6\ln(2)\cdot e^{x\ln(2)}=6\ln(2)\cdot 2^x)
Note that the last step should not be necesarry, however I feel that you should venture to leave your answers in the base given (unless asked to change the base, of course).
Now, the final one - |(1-3x)/2|. I'm going to break this up:
Now we can diff it, remembering what points are differentiable and which aren't (notice the domains for the hybrid!!):
=\left\{\begin{array}{lr}\frac{-3}{2},&x<\frac{1}{3}\\ \frac{3}{2},&x> \frac{1}{3}\end{array}\right.)
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