Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
-
¿Cómo usar?
- Derivada de:
-
Derivada de (4-3x)^7
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Derivada de π/x
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Derivada de (√x)
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Derivada de (x+7)*x^2
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Expresiones idénticas
- |x|*sqrt(x)* tres *(cuatro -x^ dos)/(dos *x^ cuatro *sqrt((tres x^ dos - cuatro)/x^3))
- módulo de x| multiplicar por raíz cuadrada de (x) multiplicar por 3 multiplicar por (4 menos x al cuadrado ) dividir por (2 multiplicar por x en el grado 4 multiplicar por raíz cuadrada de ((3x al cuadrado menos 4) dividir por x al cubo ))
- módulo de x| multiplicar por raíz cuadrada de (x) multiplicar por tres multiplicar por (cuatro menos x en el grado dos) dividir por (dos multiplicar por x en el grado cuatro multiplicar por raíz cuadrada de ((tres x en el grado dos menos cuatro) dividir por x al cubo ))
- |x|*√(x)*3*(4-x^2)/(2*x^4*√((3x^2-4)/x^3))
- |x|*sqrt(x)*3*(4-x2)/(2*x4*sqrt((3x2-4)/x3))
- |x|*sqrtx*3*4-x2/2*x4*sqrt3x2-4/x3
- |x|*sqrt(x)*3*(4-x²)/(2*x⁴*sqrt((3x²-4)/x³))
- |x|*sqrt(x)*3*(4-x en el grado 2)/(2*x en el grado 4*sqrt((3x en el grado 2-4)/x en el grado 3))
- |x|sqrt(x)3(4-x^2)/(2x^4sqrt((3x^2-4)/x^3))
- |x|sqrt(x)3(4-x2)/(2x4sqrt((3x2-4)/x3))
- |x|sqrtx34-x2/2x4sqrt3x2-4/x3
- |x|sqrtx34-x^2/2x^4sqrt3x^2-4/x^3
- |x|*sqrt(x)*3*(4-x^2) dividir por (2*x^4*sqrt((3x^2-4) dividir por x^3))
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Expresiones semejantes
- |x|*sqrt(x)*3*(4+x^2)/(2*x^4*sqrt((3x^2-4)/x^3))
- |x|*sqrt(x)*3*(4-x^2)/(2*x^4*sqrt((3x^2+4)/x^3))
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(log(6*x-1))
- sqrt(x)-1/sqrt(x)
- sqrt(acos(1-(1)/x))^(3)
- sqrt(a^2+x^2)/sqrt(a^2-x^2)
- sqrt(4-8*x)
- Raíz cuadrada sqrt
- sqrt(log(6*x-1))
- sqrt(x)-1/sqrt(x)
- sqrt(acos(1-(1)/x))^(3)
- sqrt(a^2+x^2)/sqrt(a^2-x^2)
- sqrt(4-8*x)
- Módulo |
- |x|/(x^2+1)
- |x|(exp(x)-1)
- |x|*e^-|x|
- |x*e^(-x)|
- |x|*exp(x)
Derivada de |x|*sqrt(x)*3*(4-x^2)/(2*x^4*sqrt((3x^2-4)/x^3))
Solución
Ha introducido
[src]
___ / 2\
|x|*\/ x *3*\4 - x /
---------------------
__________
/ 2
4 / 3*x - 4
2*x * / --------
/ 3
\/ x
$$\frac{3 \sqrt{x} \left|{x}\right| \left(4 - x^{2}\right)}{2 x^{4} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}}$$
(((|x|*sqrt(x))*3)*(4 - x^2))/(((2*x^4)*sqrt((3*x^2 - 4)/x^3)))
Primera derivada
[src]
/ __________ \
| / 2 / / 2 \\|
| 7 / 3*x - 4 |3*x 3*\3*x - 4/||
| __________ 2*x * / -------- *|--- - ------------||
3 | / 2 / 3 | 3 4 ||
x / 2\ | 3 / 3*x - 4 \/ x \ x 2*x /|
3*--------*\4 - x /*|- 8*x * / -------- - ------------------------------------------|*|x|
2 | / 3 2 |
1 // 2\ / ___ 3*|x| \ 3/2 \ 3*x - 4 \ \/ x 3*x - 4 /
---------------------*|\4 - x /*|3*\/ x *sign(x) + -------| - 6*x *|x|| + ----------------------------------------------------------------------------------------------
__________ | | ___| | 15/2
/ 2 \ \ 2*\/ x / / 4*x
4 / 3*x - 4
2*x * / --------
/ 3
\/ x
$$\frac{1}{2 x^{4} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}} \left(- 6 x^{\frac{3}{2}} \left|{x}\right| + \left(4 - x^{2}\right) \left(3 \sqrt{x} \operatorname{sign}{\left(x \right)} + \frac{3 \left|{x}\right|}{2 \sqrt{x}}\right)\right) + \frac{3 \frac{x^{3}}{3 x^{2} - 4} \left(4 - x^{2}\right) \left(- \frac{2 x^{7} \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x}{x^{3}} - \frac{3 \left(3 x^{2} - 4\right)}{2 x^{4}}\right)}{3 x^{2} - 4} - 8 x^{3} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}\right) \left|{x}\right|}{4 x^{\frac{15}{2}}}$$
Segunda derivada
[src]
/ / / 2 \ \ \
| | | / 2\ / / 2\\ / 2\ / 2\| | |
| |/ / 2\\ / / 2\\ | 4 | -4 + 3*x | 2 | 2*\-4 + 3*x /| 4 | -4 + 3*x | 2 | -4 + 3*x || / / 2\\ / / 2\\| |
| || 2 | -4 + 3*x || | | -4 + 3*x || ___________ | 12*x *|2 - ---------| 4*x *|5 - -------------| 3*x *|2 - ---------| 22*x *|2 - ---------|| | 2 | -4 + 3*x || | 2 | -4 + 3*x ||| |
| || 3*x *|2 - ---------|| | 3*|2 - ---------|| / 2 | | 2 | | 2 | | 2 | | 2 || ___________ | 3*x *|2 - ---------|| ___________ | 3*x *|2 - ---------||| |
| || | 2 || | | 2 || / -4 + 3*x | \ x / \ x / \ x / \ x /| / 2 / 2\ | | 2 || / 2 | | 2 ||| |
| || \ x /| |8 \ x /| 3* / --------- *|16 - --------------------- - ------------------------ + --------------------- + ---------------------| / -4 + 3*x | -4 + 3*x | | \ x /| / -4 + 3*x | \ x /|| |
| ||8 + --------------------|*|-- + -----------------| / 3 | 2 2 2 2 | 3* / --------- *|2 - ---------|*|8 + --------------------| 8* / --------- *|8 + --------------------|| |
| || 2 | | 2 2 | \/ x | / 2\ -4 + 3*x / 2\ -4 + 3*x | / 3 | 2 | | 2 | / 3 | 2 || |
| / 2\ |\ -4 + 3*x / \x -4 + 3*x / \ \-4 + 3*x / \-4 + 3*x / / \/ x \ x / \ -4 + 3*x / \/ x \ -4 + 3*x /| / / 2\\ |
| \-4 + x /*|--------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------- + ----------------------------------------------|*|x| | 2 | -4 + 3*x || |
| | ___________ 2 / 2\ 2 2 / 2\ | ___________ | 3*x *|2 - ---------|| |
| | / 2 x *\-4 + 3*x / / 2\ x *\-4 + 3*x / | / 2 | | 2 || |
| / 2\ / |x| 4*sign(x) ___ \ / |x| ___ \ ___ | 3 / -4 + 3*x \-4 + 3*x / | / -4 + 3*x | \ x /| // 2\ / |x| ___ \ 3/2 \|
| \-4 + x /*|- ---- + --------- + 8*\/ x *DiracDelta(x)| + 8*x*|----- + 2*\/ x *sign(x)| + 8*\/ x *|x| | x * / --------- | 2* / --------- *|8 + --------------------|*|\-4 + x /*|----- + 2*\/ x *sign(x)| + 4*x *|x|||
| | 3/2 ___ | | ___ | | / 3 | / 3 | 2 | | | ___ | ||
| \ x \/ x / \\/ x / \ \/ x / \/ x \ -4 + 3*x / \ \\/ x / /|
3*|- ---------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------|
| ___________ ___ 2 / 2\ |
| / 2 \/ x x *\-4 + 3*x / |
| 4 / -4 + 3*x |
| x * / --------- |
| / 3 |
\ \/ x /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
8
$$\frac{3 \left(\frac{2 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(4 x^{\frac{3}{2}} \left|{x}\right| + \left(x^{2} - 4\right) \left(2 \sqrt{x} \operatorname{sign}{\left(x \right)} + \frac{\left|{x}\right|}{\sqrt{x}}\right)\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{2} \left(3 x^{2} - 4\right)} - \frac{8 \sqrt{x} \left|{x}\right| + 8 x \left(2 \sqrt{x} \operatorname{sign}{\left(x \right)} + \frac{\left|{x}\right|}{\sqrt{x}}\right) + \left(x^{2} - 4\right) \left(8 \sqrt{x} \delta\left(x\right) + \frac{4 \operatorname{sign}{\left(x \right)}}{\sqrt{x}} - \frac{\left|{x}\right|}{x^{\frac{3}{2}}}\right)}{x^{4} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}} - \frac{\left(x^{2} - 4\right) \left(\frac{3 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{8 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{2} \left(3 x^{2} - 4\right)} - \frac{3 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} - \frac{12 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{22 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} - \frac{4 x^{2} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + 16\right)}{x^{2} \left(3 x^{2} - 4\right)} + \frac{\left(\frac{3 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + \frac{8}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{3} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}}\right) \left|{x}\right|}{\sqrt{x}}\right)}{8}$$
Tercera derivada
[src]
/ / / 2 \ \ \
| | | / 2\ / / 2\\ / 2\ / 2\| | |
| |/ / 2\\ / / 2\\ | 4 | -4 + 3*x | 2 | 2*\-4 + 3*x /| 4 | -4 + 3*x | 2 | -4 + 3*x || / / 2\\ / / 2\\| |
| || 2 | -4 + 3*x || | | -4 + 3*x || ___________ | 12*x *|2 - ---------| 4*x *|5 - -------------| 3*x *|2 - ---------| 22*x *|2 - ---------|| | 2 | -4 + 3*x || | 2 | -4 + 3*x ||| |
| || 3*x *|2 - ---------|| | 3*|2 - ---------|| / 2 | | 2 | | 2 | | 2 | | 2 || ___________ | 3*x *|2 - ---------|| ___________ | 3*x *|2 - ---------||| |
| || | 2 || | | 2 || / -4 + 3*x | \ x / \ x / \ x / \ x /| / 2 / 2\ | | 2 || / 2 | | 2 ||| |
| || \ x /| |8 \ x /| 3* / --------- *|16 - --------------------- - ------------------------ + --------------------- + ---------------------| / -4 + 3*x | -4 + 3*x | | \ x /| / -4 + 3*x | \ x /|| |
| ||8 + --------------------|*|-- + -----------------| / 3 | 2 2 2 2 | 3* / --------- *|2 - ---------|*|8 + --------------------| 8* / --------- *|8 + --------------------|| / / 2 \ / 2 \ / 2 \ / 2 \ / 2 3 2 \ / 2 \ \ |
| || 2 | | 2 2 | \/ x | / 2\ -4 + 3*x / 2\ -4 + 3*x | / 3 | 2 | | 2 | / 3 | 2 || |/ / 2\\ | / 2\ / 2\ / / 2\\ / 2\| | / 2\ / / 2\\ / 2\ / 2\| | / 2\ / / 2\\ / 2\ / 2\| / / 2\\ | / 2\ / / 2\\ / 2\ / 2\| | / 2\ / / 2\\ / 2\ / / 2\\ / 2\ / / 2\\ / 2\ / 2\ / 2\ / 2\ / / 2\\| | / 2\ / / 2\\ / 2\ / 2\| | |
| // 2\ / |x| ___ \ 3/2 \ |\ -4 + 3*x / \x -4 + 3*x / \ \-4 + 3*x / \-4 + 3*x / / \/ x \ x / \ -4 + 3*x / \/ x \ -4 + 3*x /| || 2 | -4 + 3*x || | | -4 + 3*x | | -4 + 3*x | | 2*\-4 + 3*x /| | -4 + 3*x || | 4 | -4 + 3*x | 2 | 2*\-4 + 3*x /| 4 | -4 + 3*x | 2 | -4 + 3*x || | 4 | -4 + 3*x | 2 | 2*\-4 + 3*x /| 4 | -4 + 3*x | 2 | -4 + 3*x || | | -4 + 3*x || | 4 | -4 + 3*x | 2 | 2*\-4 + 3*x /| 4 | -4 + 3*x | 2 | -4 + 3*x || | 4 | -4 + 3*x | 2 | 2*\-4 + 3*x /| 6 | -4 + 3*x | 2 | 10*\-4 + 3*x /| 6 | -4 + 3*x | 4 | 2*\-4 + 3*x /| 4 | -4 + 3*x | 6 | -4 + 3*x | 2 | -4 + 3*x | 4 | -4 + 3*x | | 2*\-4 + 3*x /|| / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ | 4 | -4 + 3*x | 2 | 2*\-4 + 3*x /| 4 | -4 + 3*x | 2 | -4 + 3*x || / / 2\\ / / 2\\ / / 2\\ / / 2\\| / / 2\\ |
| 3*|\-4 + x /*|----- + 2*\/ x *sign(x)| + 4*x *|x||*|--------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------- + ----------------------------------------------| || 3*x *|2 - ---------|| | 9*|2 - ---------| 36*|2 - ---------| 12*|5 - -------------| 30*|2 - ---------|| ___________ | 12*x *|2 - ---------| 4*x *|5 - -------------| 3*x *|2 - ---------| 22*x *|2 - ---------|| ___________ | 12*x *|2 - ---------| 4*x *|5 - -------------| 3*x *|2 - ---------| 22*x *|2 - ---------|| | 3*|2 - ---------|| | 12*x *|2 - ---------| 4*x *|5 - -------------| 3*x *|2 - ---------| 22*x *|2 - ---------|| ___________ | 456*x *|2 - ---------| 144*x *|5 - -------------| 108*x *|2 - ---------| 8*x *|27 - --------------| 9*x *|2 - ---------| 96*x *|5 - -------------| 126*x *|2 - ---------| 288*x *|2 - ---------| 312*x *|2 - ---------| 36*x *|2 - ---------|*|5 - -------------|| | 2 | -4 + 3*x || | | -4 + 3*x || | 2 | -4 + 3*x || | 2 | -4 + 3*x || | 2 | -4 + 3*x || ___________ | 12*x *|2 - ---------| 4*x *|5 - -------------| 3*x *|2 - ---------| 22*x *|2 - ---------|| | 2 | -4 + 3*x || | 2 | -4 + 3*x || | 2 | -4 + 3*x || | | -4 + 3*x ||| | 2 | -4 + 3*x || |
| | | ___ | | | ___________ 2 / 2\ 2 2 / 2\ | || | 2 || | | 2 | | 2 | | 2 | | 2 || / 2 | | 2 | | 2 | | 2 | | 2 || / 2 | | 2 | | 2 | | 2 | | 2 || | | 2 || | | 2 | | 2 | | 2 | | 2 || / 2 | | 2 | | 2 | | 2 | | 2 | | 2 | | 2 | | 2 | | 2 | | 2 | | 2 | | 2 || | 3*x *|2 - ---------|| | 3*|2 - ---------|| ___________ | 3*x *|2 - ---------|| ___________ | 3*x *|2 - ---------|| ___________ | 3*x *|2 - ---------|| / 2 / 2\ | | 2 | | 2 | | 2 | | 2 || ___________ | 3*x *|2 - ---------|| ___________ | 3*x *|2 - ---------|| | 3*x *|2 - ---------|| | 3*|2 - ---------||| ___________ | 3*x *|2 - ---------|| |
| \ \\/ x / / | / 2 x *\-4 + 3*x / / 2\ x *\-4 + 3*x / | || \ x /| |80 \ x / \ x / \ x / \ x /| / -4 + 3*x | \ x / \ x / \ x / \ x /| / -4 + 3*x | \ x / \ x / \ x / \ x /| |8 \ x /| | \ x / \ x / \ x / \ x /| / -4 + 3*x | \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x / \ x /| | | 2 || | | 2 || / 2 / 2\ | | 2 || / 2 | | 2 || / 2 | | 2 || / -4 + 3*x | -4 + 3*x | | \ x / \ x / \ x / \ x /| / 2 / 2\ | | 2 || / 2 / / 2\\ | | 2 || / 2\ | | 2 || | | 2 ||| / 2 | | 2 || |
| / 2\ / 6*sign(x) 3*|x| ___ 24*DiracDelta(x)\ / |x| 4*sign(x) ___ \ 24*|x| ___ | 3 / -4 + 3*x \-4 + 3*x / | ||8 + --------------------|*|-- + ------------------ + ------------------ + ---------------------- + ------------------| 54* / --------- *|16 - --------------------- - ------------------------ + --------------------- + ---------------------| 36* / --------- *|16 - --------------------- - ------------------------ + --------------------- + ---------------------| 3*|-- + -----------------|*|16 - --------------------- - ------------------------ + --------------------- + ---------------------| 3* / --------- *|64 - ---------------------- - -------------------------- - ----------------------- + -------------------------- + --------------------- + ------------------------- + ----------------------- + ---------------------- + ---------------------- - -----------------------------------------| | \ x /| |8 \ x /| / -4 + 3*x | -4 + 3*x | | \ x /| / -4 + 3*x | \ x /| / -4 + 3*x | \ x /| 9* / --------- *|2 - ---------|*|16 - --------------------- - ------------------------ + --------------------- + ---------------------| / -4 + 3*x | -4 + 3*x | | \ x /| / -4 + 3*x | 2*\-4 + 3*x /| | \ x /| | -4 + 3*x | | \ x /| |8 \ x /|| / -4 + 3*x | \ x /| // 2\ / |x| 4*sign(x) ___ \ / |x| ___ \ ___ \|
| \-4 + x /*|- --------- + ----- + 16*\/ x *DiracDelta(x, 1) + ----------------| + 12*x*|- ---- + --------- + 8*\/ x *DiracDelta(x)| + ------ + 48*\/ x *sign(x) | x * / --------- | || 2 | | 4 2 2 2 / 2\ 2 / 2\ | / 3 | 2 2 2 2 | / 3 | 2 2 2 2 | | 2 2 | | 2 2 2 2 | / 3 | 2 2 3 2 3 2 2 3 2 2 | 8*|8 + --------------------|*|-- + -----------------| 72* / --------- *|2 - ---------|*|8 + --------------------| 96* / --------- *|8 + --------------------| 96* / --------- *|8 + --------------------| / 3 | 2 | | 2 2 2 2 | 12* / --------- *|2 - ---------|*|8 + --------------------| 12* / --------- *|5 - -------------|*|8 + --------------------| 3*|2 - ---------|*|8 + --------------------|*|-- + -----------------|| 3* / --------- *|8 + --------------------|*|\-4 + x /*|- ---- + --------- + 8*\/ x *DiracDelta(x)| + 8*x*|----- + 2*\/ x *sign(x)| + 8*\/ x *|x|||
| | 3/2 5/2 ___ | | 3/2 ___ | ___ | / 3 | |\ -4 + 3*x / |x / 2\ / 2\ x *\-4 + 3*x / x *\-4 + 3*x / | \/ x | / 2\ -4 + 3*x / 2\ -4 + 3*x | \/ x | / 2\ -4 + 3*x / 2\ -4 + 3*x | \x -4 + 3*x / | / 2\ -4 + 3*x / 2\ -4 + 3*x | \/ x | / 2\ -4 + 3*x / 2\ -4 + 3*x / 2\ / 2\ / 2\ / 2\ -4 + 3*x / 2\ | | 2 | | 2 2 | / 3 | 2 | | 2 | / 3 | 2 | / 3 | 2 | \/ x \ x / | / 2\ -4 + 3*x / 2\ -4 + 3*x | / 3 | 2 | | 2 | / 3 | 2 | | 2 | | 2 | | 2 | | 2 2 || / 3 | 2 | | | 3/2 ___ | | ___ | ||
| \ x x \/ x / \ x \/ x / \/ x \ \/ x / ___ / 2\ | \ \-4 + 3*x / \-4 + 3*x / / \ \-4 + 3*x / \-4 + 3*x / / \ \-4 + 3*x / \-4 + 3*x / / \ \-4 + 3*x / \-4 + 3*x / / \ \-4 + 3*x / \-4 + 3*x / \-4 + 3*x / \-4 + 3*x / \-4 + 3*x / \-4 + 3*x / \-4 + 3*x / / \ -4 + 3*x / \x -4 + 3*x / \/ x \ x / \ -4 + 3*x / \/ x \ -4 + 3*x / \/ x \ -4 + 3*x / \ \-4 + 3*x / \-4 + 3*x / / \/ x \ x / \ -4 + 3*x / \/ x \ x / \ -4 + 3*x / \ x / \ -4 + 3*x / \x -4 + 3*x /| \/ x \ -4 + 3*x / \ \ x \/ x / \\/ x / /|
3*|- -------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + \/ x *\-4 + x /*|----------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------- + --------------------------------------------------------------- + ----------------------------------------------- + ----------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------- + ------------------------------------------------------------------- + ---------------------------------------------------------------------|*|x| + -----------------------------------------------------------------------------------------------------------------------------------------------------|
| ___________ x | ___________ 4 / 2\ 2 ___________ 4 / 2\ ___________ 3 4 / 2\ 2 2 2 2 ___________ | 2 / 2\ |
| / 2 | / 2 x *\-4 + 3*x / 2 / 2\ / 2 x *\-4 + 3*x / / 2 / 2\ x *\-4 + 3*x / 2 / 2\ 2 / 2\ 2 / 2\ 2 / 2\ / 2 | x *\-4 + 3*x / |
| 4 / -4 + 3*x | 3 / -4 + 3*x x *\-4 + 3*x / 5 / -4 + 3*x 5 / -4 + 3*x \-4 + 3*x / x *\-4 + 3*x / x *\-4 + 3*x / x *\-4 + 3*x / x *\-4 + 3*x / 3 / -4 + 3*x / 2\ | |
| x * / --------- | x * / --------- x * / --------- x * / --------- x * / --------- *\-4 + 3*x / | |
| / 3 | / 3 / 3 / 3 / 3 | |
\ \/ x \ \/ x \/ x \/ x \/ x / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
16
$$\frac{3 \left(\sqrt{x} \left(x^{2} - 4\right) \left(\frac{72 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{\left(3 x^{2} - 4\right)^{3}} + \frac{12 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{2} \left(3 x^{2} - 4\right)^{2}} - \frac{9 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right) \left(\frac{3 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} - \frac{12 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{22 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} - \frac{4 x^{2} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + 16\right)}{x^{2} \left(3 x^{2} - 4\right)^{2}} + \frac{12 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{2} \left(3 x^{2} - 4\right)^{2}} + \frac{96 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{2} \left(3 x^{2} - 4\right)^{2}} - \frac{36 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} - \frac{12 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{22 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} - \frac{4 x^{2} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + 16\right)}{x^{2} \left(3 x^{2} - 4\right)^{2}} + \frac{3 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right) \left(\frac{3 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + \frac{8}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{3} \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(3 x^{2} - 4\right)} + \frac{\left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right) \left(\frac{9 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} + \frac{36 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{30 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{x^{2} \left(3 x^{2} - 4\right)} + \frac{12 \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{x^{2} \left(3 x^{2} - 4\right)} + \frac{80}{x^{4}}\right)}{x^{3} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}} + \frac{96 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{4} \left(3 x^{2} - 4\right)} - \frac{54 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} - \frac{12 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{22 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} - \frac{4 x^{2} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + 16\right)}{x^{4} \left(3 x^{2} - 4\right)} + \frac{3 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{9 x^{6} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{3}}{\left(3 x^{2} - 4\right)^{3}} - \frac{108 x^{6} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{3}} + \frac{288 x^{6} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{3}} + \frac{126 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} - \frac{36 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right) \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} - \frac{456 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{96 x^{4} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{312 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} - \frac{144 x^{2} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + \frac{8 x^{2} \left(27 - \frac{10 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + 64\right)}{x^{4} \left(3 x^{2} - 4\right)} + \frac{8 \left(\frac{3 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + \frac{8}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{5} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}} - \frac{3 \left(\frac{3 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + \frac{8}{x^{2}}\right) \left(\frac{3 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} - \frac{12 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{22 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} - \frac{4 x^{2} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + 16\right)}{x^{5} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}}\right) \left|{x}\right| - \frac{3 \left(4 x^{\frac{3}{2}} \left|{x}\right| + \left(x^{2} - 4\right) \left(2 \sqrt{x} \operatorname{sign}{\left(x \right)} + \frac{\left|{x}\right|}{\sqrt{x}}\right)\right) \left(\frac{3 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{8 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{2} \left(3 x^{2} - 4\right)} - \frac{3 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)^{2}}{\left(3 x^{2} - 4\right)^{2}} - \frac{12 x^{4} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{\left(3 x^{2} - 4\right)^{2}} + \frac{22 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} - \frac{4 x^{2} \left(5 - \frac{2 \left(3 x^{2} - 4\right)}{x^{2}}\right)}{3 x^{2} - 4} + 16\right)}{x^{2} \left(3 x^{2} - 4\right)} + \frac{\left(\frac{3 \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + \frac{8}{x^{2}}\right) \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right)}{x^{3} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}}\right)}{x} + \frac{3 \sqrt{\frac{3 x^{2} - 4}{x^{3}}} \left(\frac{3 x^{2} \left(2 - \frac{3 x^{2} - 4}{x^{2}}\right)}{3 x^{2} - 4} + 8\right) \left(8 \sqrt{x} \left|{x}\right| + 8 x \left(2 \sqrt{x} \operatorname{sign}{\left(x \right)} + \frac{\left|{x}\right|}{\sqrt{x}}\right) + \left(x^{2} - 4\right) \left(8 \sqrt{x} \delta\left(x\right) + \frac{4 \operatorname{sign}{\left(x \right)}}{\sqrt{x}} - \frac{\left|{x}\right|}{x^{\frac{3}{2}}}\right)\right)}{x^{2} \left(3 x^{2} - 4\right)} - \frac{48 \sqrt{x} \operatorname{sign}{\left(x \right)} + 12 x \left(8 \sqrt{x} \delta\left(x\right) + \frac{4 \operatorname{sign}{\left(x \right)}}{\sqrt{x}} - \frac{\left|{x}\right|}{x^{\frac{3}{2}}}\right) + \left(x^{2} - 4\right) \left(16 \sqrt{x} \delta^{\left( 1 \right)}\left( x \right) + \frac{24 \delta\left(x\right)}{\sqrt{x}} - \frac{6 \operatorname{sign}{\left(x \right)}}{x^{\frac{3}{2}}} + \frac{3 \left|{x}\right|}{x^{\frac{5}{2}}}\right) + \frac{24 \left|{x}\right|}{\sqrt{x}}}{x^{4} \sqrt{\frac{3 x^{2} - 4}{x^{3}}}}\right)}{16}$$