Derivative of a split function We have the function:
$$f(x) = \frac{x^2\sqrt[4]{x^3}}{x^3+2}.$$
I rewrote it as
$$f(x) = \frac{x^2{x^{3/4}}}{x^3+2}.$$
After a while of differentiating I get the final answer:
$$f(x)= \frac{- {\sqrt[4]{\left(\frac{1}{4}\right)^{19}} + \sqrt[4]{5.5^7}}}{(x^3+2)^2}$$(The minus isn't behind the four)
But my answer sheet gives a different answer, but they also show a wrong calculation, so I don't know what is the right answer, can you help me with this?

Although collecting powers is a good idea as suggested, things are made clearer after taking formal logarithm before differentiating:
$$\ln f=2\ln x+\frac{3}{4}\ln x -\ln(x^3+2)$$
$$\frac{f'}{f}=\frac{2}{x}+\frac{3}{4x}-\frac{3x^2}{x^3+2}=\frac{11}{4x}-\frac{3x^2}{x^3+2}=-\frac{x^3-22}{4x(x^3+3)}$$
$$f'=-\frac{x^\frac{11}{4}(x^3-22)}{4x(x^3+2)^2}$$
