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
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¿Cómo usar?
- Derivada de:
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Derivada de (3x^4-x)^7
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Derivada de (3x+6)^2
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Derivada de (1+cos(x))/(1-cos(x))
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Derivada de (2*x-9)/(x-5)
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Expresiones idénticas
- x*(x+ uno)/((x+ tres)*(x*(x+ dos)^ dos)^(uno / tres))
- x multiplicar por (x más 1) dividir por ((x más 3) multiplicar por (x multiplicar por (x más 2) al cuadrado ) en el grado (1 dividir por 3))
- x multiplicar por (x más uno) dividir por ((x más tres) multiplicar por (x multiplicar por (x más dos) en el grado dos) en el grado (uno dividir por tres))
- x*(x+1)/((x+3)*(x*(x+2)2)(1/3))
- x*x+1/x+3*x*x+221/3
- x*(x+1)/((x+3)*(x*(x+2)²)^(1/3))
- x*(x+1)/((x+3)*(x*(x+2) en el grado 2) en el grado (1/3))
- x(x+1)/((x+3)(x(x+2)^2)^(1/3))
- x(x+1)/((x+3)(x(x+2)2)(1/3))
- xx+1/x+3xx+221/3
- xx+1/x+3xx+2^2^1/3
- x*(x+1) dividir por ((x+3)*(x*(x+2)^2)^(1 dividir por 3))
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Expresiones semejantes
- x*(x-1)/((x+3)*(x*(x+2)^2)^(1/3))
- x*(x+1)/((x+3)*(x*(x-2)^2)^(1/3))
- x*(x+1)/((x-3)*(x*(x+2)^2)^(1/3))
Derivada de x*(x+1)/((x+3)*(x*(x+2)^2)^(1/3))
Solución
Ha introducido
[src]
x*(x + 1)
-----------------------
____________
3 / 2
(x + 3)*\/ x*(x + 2)
$$\frac{x \left(x + 1\right)}{\sqrt[3]{x \left(x + 2\right)^{2}} \left(x + 3\right)}$$
(x*(x + 1))/(((x + 3)*(x*(x + 2)^2)^(1/3)))
Primera derivada
[src]
/ / 2 \\
| 2/3 |(x + 2) x*(4 + 2*x)||
| ____________ |x + 2| *(x + 3)*|-------- + -----------||
3 ___ | 3 / 2 \ 3 3 /|
\/ x *(x + 1)*|- \/ x*(x + 2) - -------------------------------------------|
| 2/3 2 |
1 \ x *(x + 2) /
------------------------*(1 + 2*x) + -------------------------------------------------------------------------------
3 ___ 2/3 2 4/3
\/ x *(x + 3)*|x + 2| (x + 3) *|x + 2|
$$\frac{\sqrt[3]{x} \left(x + 1\right) \left(- \sqrt[3]{x \left(x + 2\right)^{2}} - \frac{\left(x + 3\right) \left(\frac{x \left(2 x + 4\right)}{3} + \frac{\left(x + 2\right)^{2}}{3}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x + 2\right)^{2}}\right)}{\left(x + 3\right)^{2} \left|{x + 2}\right|^{\frac{4}{3}}} + \frac{1}{\sqrt[3]{x} \left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}} \left(2 x + 1\right)$$
Segunda derivada
[src]
/ / 2/3 2/3 2/3 \\
| 3 ___ (2 + 3*x)*(3 + x) / 3 ___ (2 + 3*x)*(3 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ | 2/3 (2 + 3*x)*(3 + x)*sign(2 + x) |2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(3 + x)*(4 + 3*x)||
|3*\/ x + ----------------- 3*|3*\/ x + -----------------| 2*|3*\/ x + -----------------|*sign(2 + x) 2*|3*|2 + x| *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------||
| 2/3 | 2/3 | | 2/3 | | 3 _________ x 2 + x 2 + x ||
/ 3 ___ (2 + 3*x)*(3 + x)\ 3 ___ | x *(2 + x) / 3 ___ (2 + 3*x)*(3 + x)\ /1 3 2*sign(2 + x)\ \ x *(2 + x) / \ x *(2 + x) / \ \/ |2 + x| /|
2*(1 + 2*x)*|3*\/ x + -----------------| \/ x *(1 + x)*|--------------------------- + |3*\/ x + -----------------|*|- + ----- + -------------| + ------------------------------- + ------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------|
| 2/3 | | x | 2/3 | \x 3 + x |2 + x| / 3 + x |2 + x| 2/3 2/3 |
2 \ x *(2 + x) / \ \ x *(2 + x) / x *(2 + x)*|2 + x| /
----- - ----------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 ___ 2/3 9*(3 + x)
\/ x 3*x *(3 + x)
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2/3
(3 + x)*|2 + x|
$$\frac{\frac{\sqrt[3]{x} \left(x + 1\right) \left(\left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) + \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x + 3} + \frac{3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}}{x} - \frac{2 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}\right)}{9 \left(x + 3\right)} + \frac{2}{\sqrt[3]{x}} - \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(2 x + 1\right)}{3 x^{\frac{2}{3}} \left(x + 3\right)}}{\left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}}$$
Tercera derivada
[src]
/ / 2/3 2/3 2/3 \ / 2/3 2/3 2/3 2/3 2 2/3 2/3 2/3 2/3 2/3 \ / 2/3 2/3 2/3 \ / 2/3 2/3 2/3 \ / 2/3 2/3 2/3 \\ / / 2/3 2/3 2/3 \\
| / 3 ___ (2 + 3*x)*(3 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ /1 3 2*sign(2 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ /1 3 2*sign(2 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ 2 / 3 ___ (2 + 3*x)*(3 + x)\ | 2/3 (2 + 3*x)*(3 + x)*sign(2 + x) |2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(3 + x)*(4 + 3*x)| | 27*|2 + x| *(2 + 3*x) 9*|2 + x| *(2 + 3*x) 9*(2 + 3*x)*sign(2 + x) 27*|2 + x| *(3 + x) 27*|2 + x| *(4 + 3*x) sign (2 + x)*(2 + 3*x)*(3 + x) 36*|2 + x| *(3 + x)*(4 + 3*x) 5*|2 + x| *(2 + 3*x)*(3 + x) 6*(2 + 3*x)*(3 + x)*DiracDelta(2 + x) 27*|2 + x| *(2 + 3*x)*(3 + x) 12*|2 + x| *(3 + x)*(4 + 3*x) 12*(2 + 3*x)*(3 + x)*sign(2 + x) 4*(2 + 3*x)*(3 + x)*sign(2 + x) 12*|2 + x| *(2 + 3*x)*(3 + x) 12*(3 + x)*(4 + 3*x)*sign(2 + x)| / 3 ___ (2 + 3*x)*(3 + x)\ /1 3 2*sign(2 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ | 2/3 (2 + 3*x)*(3 + x)*sign(2 + x) |2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(3 + x)*(4 + 3*x)| | 2/3 (2 + 3*x)*(3 + x)*sign(2 + x) |2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(3 + x)*(4 + 3*x)| /1 3 2*sign(2 + x)\ | 2/3 (2 + 3*x)*(3 + x)*sign(2 + x) |2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(3 + x)*(4 + 3*x)|| | 3 ___ (2 + 3*x)*(3 + x) / 3 ___ (2 + 3*x)*(3 + x)\ / 3 ___ (2 + 3*x)*(3 + x)\ | 2/3 (2 + 3*x)*(3 + x)*sign(2 + x) |2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(2 + 3*x)*(3 + x) 3*|2 + x| *(3 + x)*(4 + 3*x)||
| 5*|3*\/ x + -----------------| 27*|3*\/ x + -----------------| |3*\/ x + -----------------|*|- + ----- + -------------| 12*|3*\/ x + -----------------|*DiracDelta(2 + x) 3*|3*\/ x + -----------------|*|- + ----- + -------------| 12*|3*\/ x + -----------------| 14*sign (2 + x)*|3*\/ x + -----------------| 6*|3*|2 + x| *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------| 2*|- ----------------------- - ---------------------- + ----------------------- + --------------------- + ----------------------- - ------------------------------ - ------------------------------- + ------------------------------ + ------------------------------------- + ------------------------------- - ------------------------------- - -------------------------------- - ------------------------------- + ------------------------------- + --------------------------------| 2*|3*\/ x + -----------------|*|- + ----- + -------------|*sign(2 + x) 8*|3*\/ x + -----------------|*sign(2 + x) 24*|3*\/ x + -----------------|*sign(2 + x) 18*|3*|2 + x| *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------| 12*|3*|2 + x| *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------|*sign(2 + x) 2*|- + ----- + -------------|*|3*|2 + x| *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------|| |3*\/ x + ----------------- 3*|3*\/ x + -----------------| 2*|3*\/ x + -----------------|*sign(2 + x) 2*|3*|2 + x| *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------||
| / 2 \ | 2/3 | | 2/3 | | 2/3 | \x 3 + x |2 + x| / | 2/3 | | 2/3 | \x 3 + x |2 + x| / | 2/3 | | 2/3 | | 3 _________ x 2 + x 2 + x | | 2 + x x 3 _________ 2 + x 2 + x 4/3 2 2 3 _________ 2 x*(2 + x) 3 _________ 3 _________ x*(2 + x) 3 _________ | | 2/3 | \x 3 + x |2 + x| / | 2/3 | | 2/3 | | 3 _________ x 2 + x 2 + x | | 3 _________ x 2 + x 2 + x | \x 3 + x |2 + x| / | 3 _________ x 2 + x 2 + x || | 2/3 | 2/3 | | 2/3 | | 3 _________ x 2 + x 2 + x ||
/ 3 ___ (2 + 3*x)*(3 + x)\ 3 ___ | / 3 ___ (2 + 3*x)*(3 + x)\ |2 9 6*DiracDelta(2 + x) 3 5*sign (2 + x) 2*sign(2 + x) 6*sign(2 + x) | \ x *(2 + x) / \ x *(2 + x) / \ x *(2 + x) / \ x *(2 + x) / \ x *(2 + x) / \ x *(2 + x) / \ x *(2 + x) / \ \/ |2 + x| / \ \/ |2 + x| |2 + x| (2 + x) x \/ |2 + x| (2 + x) (2 + x)*\/ |2 + x| x*\/ |2 + x| (2 + x)*\/ |2 + x| / \ x *(2 + x) / \ x *(2 + x) / \ x *(2 + x) / \ \/ |2 + x| / \ \/ |2 + x| / \ \/ |2 + x| /| | x *(2 + x) / 3 ___ (2 + 3*x)*(3 + x)\ /1 3 2*sign(2 + x)\ \ x *(2 + x) / \ x *(2 + x) / \ \/ |2 + x| /|
2*|3*\/ x + -----------------| \/ x *(1 + x)*|2*|3*\/ x + -----------------|*|-- + -------- - ------------------- + --------- + -------------- + ------------- + ---------------| + ------------------------------- + -------------------------------- + --------------------------------------------------------- - -------------------------------------------------- + ----------------------------------------------------------- + -------------------------------- + --------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------- + ------------------------------------------- + -------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| (1 + 2*x)*|--------------------------- + |3*\/ x + -----------------|*|- + ----- + -------------| + ------------------------------- + ------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------|
| 2/3 | | | 2/3 | | 2 2 |2 + x| x*(3 + x) 2 x*|2 + x| (3 + x)*|2 + x|| 2 2 x |2 + x| 3 + x x*(3 + x) 2 5/3 2/3 2/3 2/3 |2 + x| x*|2 + x| (3 + x)*|2 + x| 2/3 2/3 2/3 5/3 2/3 2/3 | | x | 2/3 | \x 3 + x |2 + x| / 3 + x |2 + x| 2/3 2/3 |
\ x *(2 + x) / \ \ x *(2 + x) / \x (3 + x) (2 + x) / x (3 + x) (2 + x) x *(2 + x)*|2 + x| x *(2 + x)*|2 + x| x *(2 + x)*(3 + x)*|2 + x| x *(2 + x)*|2 + x| x *(2 + x)*|2 + x| / \ \ x *(2 + x) / x *(2 + x)*|2 + x| /
- ------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2/3 27 2/3
x 3*x
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2/3
(3 + x) *|2 + x|
$$\frac{- \frac{\sqrt[3]{x} \left(x + 1\right) \left(\frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + 2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(- \frac{6 \delta\left(x + 2\right)}{\left|{x + 2}\right|} + \frac{6 \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 3\right) \left|{x + 2}\right|} + \frac{9}{\left(x + 3\right)^{2}} + \frac{5 \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left(x + 2\right)^{2}} + \frac{2 \operatorname{sign}{\left(x + 2 \right)}}{x \left|{x + 2}\right|} + \frac{3}{x \left(x + 3\right)} + \frac{2}{x^{2}}\right) - \frac{12 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \delta\left(x + 2\right)}{\left|{x + 2}\right|} + \frac{3 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right)}{x + 3} + \frac{24 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 3\right) \left|{x + 2}\right|} + \frac{27 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{\left(x + 3\right)^{2}} + \frac{14 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left(x + 2\right)^{2}} + \frac{\left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right)}{x} + \frac{8 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{x \left|{x + 2}\right|} + \frac{12 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x \left(x + 3\right)} + \frac{5 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x^{2}} - \frac{2 \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}} - \frac{12 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right) \operatorname{sign}{\left(x + 2 \right)}}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{5}{3}}} + \frac{2 \left(\frac{6 \left(x + 3\right) \left(3 x + 2\right) \delta\left(x + 2\right)}{\sqrt[3]{\left|{x + 2}\right|}} - \frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left|{x + 2}\right|^{\frac{4}{3}}} + \frac{9 \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} - \frac{12 \left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} + \frac{12 \left(x + 3\right) \left(3 x + 4\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} + \frac{27 \left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{27 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{27 \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{27 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x + 2\right)^{2}} - \frac{36 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x + 2\right)^{2}} - \frac{4 \left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{x \sqrt[3]{\left|{x + 2}\right|}} - \frac{9 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x} + \frac{12 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x + 2\right)} - \frac{12 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x + 2\right)} + \frac{5 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x^{2}}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}} - \frac{18 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}} - \frac{6 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{5}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}\right)}{27} - \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \left(\left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) + \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x + 3} + \frac{3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}}{x} - \frac{2 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}\right)}{3 x^{\frac{2}{3}}}}{\left(x + 3\right)^{2} \left|{x + 2}\right|^{\frac{2}{3}}}$$