/ |x|\ / ___ \
|1 - ---|*\\/ x - 1/
1 \ x /
------------------------- + ---------------------
/ ____ \ 2
___ | / 2 | / ____ \
2*\/ x *\\/ x - x - 1/ | / 2 |
\\/ x - x - 1/
$$\frac{\left(1 - \frac{\left|{x}\right|}{x}\right) \left(\sqrt{x} - 1\right)}{\left(\left(- x + \sqrt{x^{2}}\right) - 1\right)^{2}} + \frac{1}{2 \sqrt{x} \left(\left(- x + \sqrt{x^{2}}\right) - 1\right)}$$
/ 2\
| |x| / |x|\ |
|- --- + sign(x) 2*|1 - ---| |
|x| / ___\ | x \ x / |
1 - --- \-1 + \/ x /*|--------------- + ------------|
1 x \ x 1 + x - |x| /
------ + ------------------- - ---------------------------------------------
3/2 ___ 1 + x - |x|
4*x \/ x *(1 + x - |x|)
----------------------------------------------------------------------------
1 + x - |x|
$$\frac{- \frac{\left(\sqrt{x} - 1\right) \left(\frac{2 \left(1 - \frac{\left|{x}\right|}{x}\right)^{2}}{x - \left|{x}\right| + 1} + \frac{\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}}{x}\right)}{x - \left|{x}\right| + 1} + \frac{1 - \frac{\left|{x}\right|}{x}}{\sqrt{x} \left(x - \left|{x}\right| + 1\right)} + \frac{1}{4 x^{\frac{3}{2}}}}{x - \left|{x}\right| + 1}$$
/ |x| sign(x) 3 \
| --- - ------- + DiracDelta(x) / |x|\ / |x|\ / |x| \| / 2\
| 2 x 3*|1 - ---| 3*|1 - ---|*|- --- + sign(x)|| | |x| / |x|\ |
/ ___\ | x \ x / \ x / \ x /| |- --- + sign(x) 2*|1 - ---| |
2*\-1 + \/ x /*|- ----------------------------- + -------------- + -----------------------------| | x \ x / | / |x|\
| x 2 x*(1 + x - |x|) | 3*|--------------- + ------------| 3*|1 - ---|
3 \ (1 + x - |x|) / \ x 1 + x - |x| / \ x /
- ------ + ------------------------------------------------------------------------------------------------- - ---------------------------------- - --------------------
5/2 1 + x - |x| ___ 3/2
8*x 2*\/ x *(1 + x - |x|) 4*x *(1 + x - |x|)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 + x - |x|
$$\frac{\frac{2 \left(\sqrt{x} - 1\right) \left(\frac{3 \left(1 - \frac{\left|{x}\right|}{x}\right)^{3}}{\left(x - \left|{x}\right| + 1\right)^{2}} + \frac{3 \left(1 - \frac{\left|{x}\right|}{x}\right) \left(\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}\right)}{x \left(x - \left|{x}\right| + 1\right)} - \frac{\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}}{x}\right)}{x - \left|{x}\right| + 1} - \frac{3 \left(\frac{2 \left(1 - \frac{\left|{x}\right|}{x}\right)^{2}}{x - \left|{x}\right| + 1} + \frac{\operatorname{sign}{\left(x \right)} - \frac{\left|{x}\right|}{x}}{x}\right)}{2 \sqrt{x} \left(x - \left|{x}\right| + 1\right)} - \frac{3 \left(1 - \frac{\left|{x}\right|}{x}\right)}{4 x^{\frac{3}{2}} \left(x - \left|{x}\right| + 1\right)} - \frac{3}{8 x^{\frac{5}{2}}}}{x - \left|{x}\right| + 1}$$