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)/x^2
-
Derivada de 2/x²
-
Derivada de -2*y
-
Derivada de 3/2x
-
Expresiones idénticas
- xln|x+√x^ dos + tres |-√x^ dos + tres
- xln módulo de x más √x al cuadrado más 3| menos √x al cuadrado más 3
- xln módulo de x más √x en el grado dos más tres | menos √x en el grado dos más tres
- xln|x+√x2+3|-√x2+3
- xln|x+√x²+3|-√x²+3
- xln|x+√x en el grado 2+3|-√x en el grado 2+3
-
Expresiones semejantes
- xln|x+√x^2+3|-√x^2-3
- xln|x+√x^2-3|-√x^2+3
- xln|x-√x^2+3|-√x^2+3
- xln|x+√x^2+3|+√x^2+3
-
Expresiones con funciones
- xln
- xln(x+√x2−1)
- xln|x+(x^2+3)^(1/2)|-(x^2+3)^(1/2)
- xln(x)/ln(3)
- xln(x/p)+(1-x)ln((1-x)/(1-p))
- xln|(x+sqtr(x^2+3))|-sqrt(x^2+3)
- Módulo |
- |x|:x
- |x|((x^2)-pi^2)^2
- ||x|-|x-11||
- |x-t|
- |x|/sin(x)*cos(x)
Derivada de xln|x+√x^2+3|-√x^2+3
Solución
Ha introducido
[src]
/| 2 |\ 2
|| ___ || ___
x*log\|x + \/ x + 3|/ - \/ x + 3
$$\left(- \left(\sqrt{x}\right)^{2} + x \log{\left(\left|{\left(\left(\sqrt{x}\right)^{2} + x\right) + 3}\right| \right)}\right) + 3$$
x*log(Abs(x + (sqrt(x))^2 + 3)) - (sqrt(x))^2 + 3
Primera derivada
[src]
/ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \
| | x*cos |-----------| x*sin |-----------|| |
|/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\|
x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x) /| 2 |\
\\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // || ___ ||
-1 + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + log\|x + \/ x + 3|/
| 2 |
| ___ |
(3 + 2*x)*|x + \/ x + 3|
$$\frac{x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{\left(\left(\sqrt{x}\right)^{2} + x\right) + 3}\right|} + \log{\left(\left|{\left(\left(\sqrt{x}\right)^{2} + x\right) + 3}\right| \right)} - 1$$
Segunda derivada
[src]
/ / 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ \ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ 2
/ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ | | cos |-----------| sin |-----------| 2*x*cos |-----------|*DiracDelta(x) 2*x*sin |-----------|*DiracDelta(x)| | x*cos |-----------| x*sin |-----------|| | / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \
| | x*cos |-----------| x*sin |-----------|| | |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 / \ 2 / \ 2 / | 2/atan2(0, x)\ 2/atan2(0, x)\ / 2/atan2(0, x)\ 2/atan2(0, x)\\ | \ 2 / \ 2 /| | | | x*cos |-----------| x*sin |-----------|| | | | x*cos |-----------| x*sin |-----------|| | | | x*cos |-----------| x*sin |-----------|| |
|/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*sign(3 + 2*x) |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| 2 |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\|
2*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x) |\ \ 2 / \ 2 / / | sign(x) sign(x) 2 2 | \ 2 / \ 2 / \ \ 2 / \ 2 // \ sign(x) sign(x) / | x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x) 4*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x) 2*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x)
\\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \ \ sign (x) sign (x) / / \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
|3 + 2*x| |3 + 2*x| 3 |3 + 2*x| (3 + 2*x)*|3 + 2*x|
(3 + 2*x)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 + 2*x
$$\frac{\frac{4 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta\left(2 x + 3\right)}{\left|{2 x + 3}\right|} + \frac{x \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|} - \frac{2 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{2 x + 3}\right|} - \frac{x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}} + \frac{2 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|}}{2 x + 3}$$
Tercera derivada
[src]
/ / 2 2/atan2(0, x)\ 2 2/atan2(0, x)\\ \
| | 4*x*DiracDelta (x)*cos |-----------| 4*x*DiracDelta (x)*sin |-----------|| |
2 / / 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ \ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ \ 2 / \ 2 /| / 2/atan2(0, x)\ 2/atan2(0, x)\\ / 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | 2 / / 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ \ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ 2 / / 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ \ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ 2/atan2(0, x)\ \ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ 3
/ / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ | | cos |-----------| sin |-----------| 2*x*cos |-----------|*DiracDelta(x) 2*x*sin |-----------|*DiracDelta(x)| | x*cos |-----------| x*sin |-----------|| | / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ ||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|- 2*sin |-----------|*DiracDelta(x) + 2*cos |-----------|*DiracDelta(x) + x*cos |-----------|*DiracDelta(x, 1) - x*sin |-----------|*DiracDelta(x, 1) - ------------------------------------ + ------------------------------------| | x*cos |-----------| x*sin |-----------|| | cos |-----------| sin |-----------| 2*x*cos |-----------|*DiracDelta(x) 2*x*sin |-----------|*DiracDelta(x)| | / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ | | cos |-----------| sin |-----------| 2*x*cos |-----------|*DiracDelta(x) 2*x*sin |-----------|*DiracDelta(x)| | x*cos |-----------| x*sin |-----------|| | / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ | | cos |-----------| sin |-----------| 2*x*cos |-----------|*DiracDelta(x) 2*x*sin |-----------|*DiracDelta(x)| | x*cos |-----------| x*sin |-----------|| | | | x*cos |-----------| x*sin |-----------|| | | | cos |-----------| sin |-----------| 2*x*cos |-----------|*DiracDelta(x) 2*x*sin |-----------|*DiracDelta(x)| | x*cos |-----------| x*sin |-----------|| | / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \ / / 2/atan2(0, x)\ 2/atan2(0, x)\\ \
| | x*cos |-----------| x*sin |-----------|| | |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 / \ 2 / \ 2 / | 2/atan2(0, x)\ 2/atan2(0, x)\ / 2/atan2(0, x)\ 2/atan2(0, x)\\ | \ 2 / \ 2 /| | | | x*cos |-----------| x*sin |-----------|| | | | x*cos |-----------| x*sin |-----------|| | |\ \ 2 / \ 2 / / \ \ 2 / \ 2 / \ 2 / \ 2 / sign(x) sign(x) / / 2/atan2(0, x)\ 2/atan2(0, x)\\ | \ 2 / \ 2 /| / 2/atan2(0, x)\ 2/atan2(0, x)\\ | \ 2 / \ 2 / \ 2 / \ 2 / | | | | x*cos |-----------| x*sin |-----------|| | | | x*cos |-----------| x*sin |-----------|| | |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 / \ 2 / \ 2 / | 2/atan2(0, x)\ 2/atan2(0, x)\ / 2/atan2(0, x)\ 2/atan2(0, x)\\ | \ 2 / \ 2 /| | | | x*cos |-----------| x*sin |-----------|| | | | x*cos |-----------| x*sin |-----------|| | |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 / \ 2 / \ 2 / | 2/atan2(0, x)\ 2/atan2(0, x)\ / 2/atan2(0, x)\ 2/atan2(0, x)\\ | \ 2 / \ 2 /| | 2 |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 / \ 2 / \ 2 / | 2/atan2(0, x)\ 2/atan2(0, x)\ / 2/atan2(0, x)\ 2/atan2(0, x)\\ | \ 2 / \ 2 /| | | | x*cos |-----------| x*sin |-----------|| | | | x*cos |-----------| x*sin |-----------|| |
|/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| 2 3*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*sign(3 + 2*x) |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| 2*x*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + |sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x, 1) + 2*|sin |-----------| - cos |-----------||*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------|*DiracDelta(x)|*sign(3 + 2*x) |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| 2 |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| 8*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*DiracDelta(3 + 2*x) |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| 4*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*sign(3 + 2*x) 3*x*sign (3 + 2*x)*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)| |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\| 3 |/ 2/atan2(0, x)\ 2/atan2(0, x)\ \ | \ 2 / \ 2 /| 2/atan2(0, x)\ 2/atan2(0, x)\|
3*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x) |\ \ 2 / \ 2 / / | sign(x) sign(x) 2 2 | \ 2 / \ 2 / \ \ 2 / \ 2 // \ sign(x) sign(x) / | 12*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x) 6*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x) | 2 \ \ 2 / \ 2 // \ sign(x) sign(x) / \ \ 2 / \ 2 // | sign(x) sign(x) 2 2 | | 6*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x) 8*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x, 1) |\ \ 2 / \ 2 / / | sign(x) sign(x) 2 2 | \ 2 / \ 2 / \ \ 2 / \ 2 // \ sign(x) sign(x) / | 16*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x) 12*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *DiracDelta(3 + 2*x)*sign(3 + 2*x) |\ \ 2 / \ 2 / / | sign(x) sign(x) 2 2 | \ 2 / \ 2 / \ \ 2 / \ 2 // \ sign(x) sign(x) / | \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // |\ \ 2 / \ 2 / / | sign(x) sign(x) 2 2 | \ 2 / \ 2 / \ \ 2 / \ 2 // \ sign(x) sign(x) / | 2*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x)*|3 + 2*x| 8*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x)
\\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \ \ sign (x) sign (x) / / \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \ sign (x) \ sign (x) sign (x) / / \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \ \ sign (x) sign (x) / / \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \ \ sign (x) sign (x) / / \ \ sign (x) sign (x) / / \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 // \\ \ 2 / \ 2 / / \ sign(x) sign(x) / \ 2 / \ 2 //
- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 |3 + 2*x| |3 + 2*x| (3 + 2*x)*|3 + 2*x| |3 + 2*x| 4 |3 + 2*x| |3 + 2*x| (3 + 2*x)*|3 + 2*x| 3 (3 + 2*x)*|3 + 2*x| 3 6 2
(3 + 2*x) (3 + 2*x) (3 + 2*x) (3 + 2*x) (3 + 2*x) (3 + 2*x) *|3 + 2*x|
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 + 2*x
$$\frac{\frac{8 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta^{\left( 1 \right)}\left( 2 x + 3 \right)}{\left|{2 x + 3}\right|} + \frac{8 x \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \delta\left(2 x + 3\right)}{\left|{2 x + 3}\right|} - \frac{2 x \left(\left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta^{\left( 1 \right)}\left( x \right) + 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) \delta\left(x\right) + \frac{\left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \left(\delta\left(x\right)\right)^{2}}{\operatorname{sign}{\left(x \right)}} - x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta^{\left( 1 \right)}\left( x \right) - \frac{4 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \left(\delta\left(x\right)\right)^{2}}{\operatorname{sign}{\left(x \right)}} + x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta^{\left( 1 \right)}\left( x \right) - 2 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right) + 2 \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)\right)}{\operatorname{sign}^{2}{\left(x \right)}}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|} - \frac{16 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta\left(2 x + 3\right)}{\left(2 x + 3\right) \left|{2 x + 3}\right|} - \frac{4 x \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{2 x + 3}\right|} + \frac{8 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{2} \left|{2 x + 3}\right|} - \frac{12 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \delta\left(2 x + 3\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}} - \frac{3 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}} + \frac{6 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{4}} + \frac{2 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{3} \left|{2 x + 3}\right| \operatorname{sign}^{3}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{6}} + \frac{12 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta\left(2 x + 3\right)}{\left|{2 x + 3}\right|} + \frac{3 \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|} - \frac{6 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{2 x + 3}\right|} - \frac{3 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}}}{2 x + 3}$$