/ ____ \
___ | / 3 2/3|
3*\/ x / ___ \ | 3*\/ x 2*|x| |
-3 + ------- \x*\/ x - 3*x/*|- --------- - --------|
2 \ x 3*x /
------------------- + ----------------------------------------
____ ____ 2
/ 3 3 / 2 / ____ ____\
2*\/ x + \/ x | / 3 3 / 2 |
\2*\/ x + \/ x /
$$\frac{\frac{3 \sqrt{x}}{2} - 3}{2 \sqrt{x^{3}} + \sqrt[3]{x^{2}}} + \frac{\left(- \frac{3 \sqrt{x^{3}}}{x} - \frac{2 \left|{x}\right|^{\frac{2}{3}}}{3 x}\right) \left(\sqrt{x} x - 3 x\right)}{\left(2 \sqrt{x^{3}} + \sqrt[3]{x^{2}}\right)^{2}}$$
/ 2\
| ____ / ____\ |
| 2/3 / 3 | 2/3 / 3 | |
/ 3/2 \ | 12*|x| 8*sign(x) 27*\/ x 4*\2*|x| + 9*\/ x / |
\x - 3*x/*|- --------- + --------- + ---------- - -------------------------|
/ ____\ | x 3 _____ x / ____\ |
/ ___\ | 2/3 / 3 | | \/ |x| | 2/3 / 3 | |
3 \-2 + \/ x /*\2*|x| + 9*\/ x / \ x*\|x| + 2*\/ x / /
------- - ----------------------------------- - -------------------------------------------------------------------------------
___ / ____\ / ____\
4*\/ x | 2/3 / 3 | | 2/3 / 3 |
x*\|x| + 2*\/ x / 18*x*\|x| + 2*\/ x /
-------------------------------------------------------------------------------------------------------------------------------
____
2/3 / 3
|x| + 2*\/ x
$$\frac{- \frac{\left(\sqrt{x} - 2\right) \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} - \frac{\left(x^{\frac{3}{2}} - 3 x\right) \left(\frac{8 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + \frac{27 \sqrt{x^{3}}}{x} - \frac{12 \left|{x}\right|^{\frac{2}{3}}}{x} - \frac{4 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)^{2}}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}\right)}{18 x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} + \frac{3}{4 \sqrt{x}}}{2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}}$$
/ / ____\\
| / ____\ | 2/3 / 3 ||
| 3 | 2/3 / 3 | | 12*|x| 8*sign(x) 27*\/ x ||
/ 2\ | ____ / ____\ 12*\2*|x| + 9*\/ x /*|- --------- + --------- + ----------||
| ____ / ____\ | | 2/3 2 / 3 | 2/3 / 3 | | x 3 _____ x ||
| 2/3 / 3 | 2/3 / 3 | | / 3/2 \ | 144*|x| 96*DiracDelta(x) 16*sign (x) 81*\/ x 24*\2*|x| + 9*\/ x / 96*sign(x) \ \/ |x| /|
/ ___\ | 12*|x| 8*sign(x) 27*\/ x 4*\2*|x| + 9*\/ x / | 2*\x - 3*x/*|- ---------- - ---------------- + ----------- + ---------- - -------------------------- + ---------- + ----------------------------------------------------------------|
54*\-2 + \/ x /*|- --------- + --------- + ---------- - -------------------------| | 2 3 _____ 4/3 2 2 3 _____ / ____\ |
/ ____\ | x 3 _____ x / ____\ | | x \/ |x| |x| x / ____\ x*\/ |x| | 2/3 / 3 | |
| 2/3 / 3 | | \/ |x| | 2/3 / 3 | | | 2 | 2/3 / 3 | x*\|x| + 2*\/ x / |
81 162*\2*|x| + 9*\/ x / \ x*\|x| + 2*\/ x / / \ x *\|x| + 2*\/ x / /
- ---- - -------------------------- - ---------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3/2 / ____\ / ____\ / ____\
x 3/2 | 2/3 / 3 | | 2/3 / 3 | | 2/3 / 3 |
x *\|x| + 2*\/ x / x*\|x| + 2*\/ x / x*\|x| + 2*\/ x /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ____\
| 2/3 / 3 |
216*\|x| + 2*\/ x /
$$\frac{- \frac{54 \left(\sqrt{x} - 2\right) \left(\frac{8 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + \frac{27 \sqrt{x^{3}}}{x} - \frac{12 \left|{x}\right|^{\frac{2}{3}}}{x} - \frac{4 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)^{2}}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} + \frac{2 \left(x^{\frac{3}{2}} - 3 x\right) \left(- \frac{96 \delta\left(x\right)}{\sqrt[3]{\left|{x}\right|}} + \frac{16 \operatorname{sign}^{2}{\left(x \right)}}{\left|{x}\right|^{\frac{4}{3}}} + \frac{96 \operatorname{sign}{\left(x \right)}}{x \sqrt[3]{\left|{x}\right|}} + \frac{12 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right) \left(\frac{8 \operatorname{sign}{\left(x \right)}}{\sqrt[3]{\left|{x}\right|}} + \frac{27 \sqrt{x^{3}}}{x} - \frac{12 \left|{x}\right|^{\frac{2}{3}}}{x}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} + \frac{81 \sqrt{x^{3}}}{x^{2}} - \frac{144 \left|{x}\right|^{\frac{2}{3}}}{x^{2}} - \frac{24 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)^{3}}{x^{2} \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)^{2}}\right)}{x \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)} - \frac{81}{x^{\frac{3}{2}}} - \frac{162 \left(9 \sqrt{x^{3}} + 2 \left|{x}\right|^{\frac{2}{3}}\right)}{x^{\frac{3}{2}} \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}}{216 \left(2 \sqrt{x^{3}} + \left|{x}\right|^{\frac{2}{3}}\right)}$$