Differentiation, an issue with an exercise I'm currently working on an exercise that involves quite a few fractional exponents. This is it: $$y = \frac {(x^4 + a)^\frac {1}{3}} {(x^3 + a)^ \frac {1}{2}} $$
I take the multiplication route by doing:
$$(x^4 + a)^ \frac{1}{3}(x^3 + a) ^ \frac {-1}{2} $$
I eventually get $$(x^4 + a)^\frac {1}{3} \frac{-3}{2}x^2(x^3 + a)^ \frac{-3}{2} + (x^3 + a)^ \frac{-1}{2}\frac{4}{3}x^3(x^4 + a)^\frac{-2}{3}$$
This is what I can't get past at the moment. I'm not sure of the next step I should take to ensure I get the correct answer. Any help on this is much appreciated as always! There may be some formatting issues with the negative fractional exponents as they do look a little odd. 

Logarithmic differentiation is useful here.  
$$\log{y} = \frac13 \log{(x^4+a)} - \frac12 \log{(x^3+a)}$$
Then
$$\frac{y'}{y} = \frac13 \frac{4 x^3}{x^4+a} - \frac12 \frac{3 x^2}{x^3+a}$$
Multiply by the original $y$ and you are done.
