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 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- ln^ dos (arctg((uno +sin(x))/(uno -cos(x))))
- ln al cuadrado (arctg((1 más seno de (x)) dividir por (1 menos coseno de (x))))
- ln en el grado dos (arctg((uno más seno de (x)) dividir por (uno menos coseno de (x))))
- ln2(arctg((1+sin(x))/(1-cos(x))))
- ln2arctg1+sinx/1-cosx
- ln²(arctg((1+sin(x))/(1-cos(x))))
- ln en el grado 2(arctg((1+sin(x))/(1-cos(x))))
- ln^2arctg1+sinx/1-cosx
- ln^2(arctg((1+sin(x)) dividir por (1-cos(x))))
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Expresiones semejantes
- ln^2(arctg((1+sin(x))/(1+cos(x))))
- ln^2(arctg((1-sin(x))/(1-cos(x))))
- ln^2(arctg((1+sinx)/(1-cosx)))
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Expresiones con funciones
- ln
- ln^2(2x-1)
- ln*(x+sqrt*(x^2+1))
- ln(√x)
- ln(x+1)/x^2
- ln(x^1/2)
- arctg
- arctg^2(1/x)
- arctg(cos(x))
- arctg(x+cosx)
- Seno sin
- sin(x)cos(x)
- sin(t)*cos(t)
- sin(3*x^2)/((3*x^2))
- sin(3*x-pi/12)
- sin(5*x+2)
- Coseno cos
- cos(3/x)
- cos(x)^sin(x)
- cos*(x^2)
- cos(x)/(e^x)
- cos(x+3)
Derivada de ln^2(arctg((1+sin(x))/(1-cos(x))))
Solución
Ha introducido
[src]
2/ /1 + sin(x)\\
log |atan|----------||
\ \1 - cos(x)//
$$\log{\left(\operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}} \right)} \right)}^{2}$$
log(atan((1 + sin(x))/(1 - cos(x))))^2
Primera derivada
[src]
/ cos(x) (1 + sin(x))*sin(x)\ / /1 + sin(x)\\
2*|---------- - -------------------|*log|atan|----------||
|1 - cos(x) 2 | \ \1 - cos(x)//
\ (1 - cos(x)) /
----------------------------------------------------------
/ 2\
| (1 + sin(x)) | /1 + sin(x)\
|1 + -------------|*atan|----------|
| 2| \1 - cos(x)/
\ (1 - cos(x)) /
$$\frac{2 \left(\frac{\cos{\left(x \right)}}{1 - \cos{\left(x \right)}} - \frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\left(1 - \cos{\left(x \right)}\right)^{2}}\right) \log{\left(\operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}} \right)} \right)}}{\left(1 + \frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(1 - \cos{\left(x \right)}\right)^{2}}\right) \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{1 - \cos{\left(x \right)}} \right)}}$$
Segunda derivada
[src]
/ 2 2 2 \
| /(1 + sin(x))*sin(x) \ /(1 + sin(x))*sin(x) \ / / 1 + sin(x)\\ /(1 + sin(x))*sin(x) \ / / 1 + sin(x)\\|
|/ 2 \ |------------------- + cos(x)| |------------------- + cos(x)| *log|-atan|-----------|| 2*|------------------- + cos(x)| *(1 + sin(x))*log|-atan|-----------|||
|| (1 + sin(x))*cos(x) 2*cos(x)*sin(x) 2*sin (x)*(1 + sin(x))| / / 1 + sin(x)\\ \ -1 + cos(x) / \ -1 + cos(x) / \ \-1 + cos(x)// \ -1 + cos(x) / \ \-1 + cos(x)//|
2*||-sin(x) + ------------------- + --------------- + ----------------------|*log|-atan|-----------|| + ---------------------------------------------------- - ------------------------------------------------------- - ----------------------------------------------------------------------|
|| -1 + cos(x) -1 + cos(x) 2 | \ \-1 + cos(x)// / 2 \ / 2 \ / 2 \ |
|\ (-1 + cos(x)) / | (1 + sin(x)) | / 1 + sin(x)\ | (1 + sin(x)) | / 1 + sin(x)\ | (1 + sin(x)) | 2 |
| |1 + --------------|*(-1 + cos(x))*atan|-----------| |1 + --------------|*(-1 + cos(x))*atan|-----------| |1 + --------------|*(-1 + cos(x)) |
| | 2| \-1 + cos(x)/ | 2| \-1 + cos(x)/ | 2| |
\ \ (-1 + cos(x)) / \ (-1 + cos(x)) / \ (-1 + cos(x)) / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 \
| (1 + sin(x)) | / 1 + sin(x)\
|1 + --------------|*(-1 + cos(x))*atan|-----------|
| 2| \-1 + cos(x)/
\ (-1 + cos(x)) /
$$\frac{2 \left(\left(\frac{\left(\sin{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{2 \left(\sin{\left(x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \sin{\left(x \right)} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} - 1}\right) \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)} - \frac{2 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{2} \left(\sin{\left(x \right)} + 1\right) \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right)^{2}} - \frac{\left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{2} \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right) \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}} + \frac{\left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{2}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right) \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}}\right)}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right) \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}}$$
Tercera derivada
[src]
/ / 2 2 2 \ / 2 \ / 2 \ / 2 \ \
| 3 3 /(1 + sin(x))*sin(x) \ | 2 (1 + sin(x)) *cos(x) 3*(1 + sin(x)) *sin (x) 4*(1 + sin(x))*cos(x)*sin(x)| / / 1 + sin(x)\\ 3 /(1 + sin(x))*sin(x) \ | (1 + sin(x))*cos(x) 2*cos(x)*sin(x) 2*sin (x)*(1 + sin(x))| 3 /(1 + sin(x))*sin(x) \ | (1 + sin(x))*cos(x) 2*cos(x)*sin(x) 2*sin (x)*(1 + sin(x))| / / 1 + sin(x)\\ /(1 + sin(x))*sin(x) \ | (1 + sin(x))*cos(x) 2*cos(x)*sin(x) 2*sin (x)*(1 + sin(x))| / / 1 + sin(x)\\ 3 |
| /(1 + sin(x))*sin(x) \ /(1 + sin(x))*sin(x) \ 2*|------------------- + cos(x)|*|cos (x) - (1 + sin(x))*sin(x) + -------------------- + ----------------------- + ----------------------------|*log|-atan|-----------|| /(1 + sin(x))*sin(x) \ / / 1 + sin(x)\\ 3*|------------------- + cos(x)|*|-sin(x) + ------------------- + --------------- + ----------------------| 2 /(1 + sin(x))*sin(x) \ / / 1 + sin(x)\\ 4*(1 + sin(x))*|------------------- + cos(x)|*|-sin(x) + ------------------- + --------------- + ----------------------|*log|-atan|-----------|| 3*|------------------- + cos(x)|*|-sin(x) + ------------------- + --------------- + ----------------------|*log|-atan|-----------|| /(1 + sin(x))*sin(x) \ / / 1 + sin(x)\\|
|/ 2 2 3 2 \ 3*|------------------- + cos(x)| 6*|------------------- + cos(x)| *(1 + sin(x)) \ -1 + cos(x) / | -1 + cos(x) 2 -1 + cos(x) | \ \-1 + cos(x)// 2*|------------------- + cos(x)| *log|-atan|-----------|| \ -1 + cos(x) / | -1 + cos(x) -1 + cos(x) 2 | 8*(1 + sin(x)) *|------------------- + cos(x)| *log|-atan|-----------|| \ -1 + cos(x) / | -1 + cos(x) -1 + cos(x) 2 | \ \-1 + cos(x)// \ -1 + cos(x) / | -1 + cos(x) -1 + cos(x) 2 | \ \-1 + cos(x)// 6*|------------------- + cos(x)| *(1 + sin(x))*log|-atan|-----------|||
|| 3*sin (x) 3*cos (x) (1 + sin(x))*sin(x) 6*sin (x)*(1 + sin(x)) 6*sin (x)*cos(x) 6*(1 + sin(x))*cos(x)*sin(x)| / / 1 + sin(x)\\ \ -1 + cos(x) / \ -1 + cos(x) / \ (-1 + cos(x)) / \ -1 + cos(x) / \ \-1 + cos(x)// \ (-1 + cos(x)) / \ -1 + cos(x) / \ \-1 + cos(x)// \ (-1 + cos(x)) / \ (-1 + cos(x)) / \ -1 + cos(x) / \ \-1 + cos(x)//|
2*||-cos(x) - ----------- + ----------- - ------------------- + ---------------------- + ---------------- + ----------------------------|*log|-atan|-----------|| - ------------------------------------------------------- - ------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------|
|| -1 + cos(x) -1 + cos(x) -1 + cos(x) 3 2 2 | \ \-1 + cos(x)// 2 2 / 2 \ 2 / 2 \ 2 / 2 \ / 2 \ 2 |
|\ (-1 + cos(x)) (-1 + cos(x)) (-1 + cos(x)) / / 2 \ / 2 \ | (1 + sin(x)) | 2 / 2 \ | (1 + sin(x)) | / 1 + sin(x)\ / 2 \ | (1 + sin(x)) | 2 | (1 + sin(x)) | / 1 + sin(x)\ / 2 \ |
| | (1 + sin(x)) | 2 2/ 1 + sin(x)\ | (1 + sin(x)) | 3 / 1 + sin(x)\ |1 + --------------|*(-1 + cos(x)) | (1 + sin(x)) | 2 2/ 1 + sin(x)\ |1 + --------------|*(-1 + cos(x))*atan|-----------| | (1 + sin(x)) | 4 |1 + --------------|*(-1 + cos(x)) |1 + --------------|*(-1 + cos(x))*atan|-----------| | (1 + sin(x)) | 3 / 1 + sin(x)\ |
| |1 + --------------| *(-1 + cos(x)) *atan |-----------| |1 + --------------| *(-1 + cos(x)) *atan|-----------| | 2| |1 + --------------| *(-1 + cos(x)) *atan |-----------| | 2| \-1 + cos(x)/ |1 + --------------| *(-1 + cos(x)) | 2| | 2| \-1 + cos(x)/ |1 + --------------| *(-1 + cos(x)) *atan|-----------| |
| | 2| \-1 + cos(x)/ | 2| \-1 + cos(x)/ \ (-1 + cos(x)) / | 2| \-1 + cos(x)/ \ (-1 + cos(x)) / | 2| \ (-1 + cos(x)) / \ (-1 + cos(x)) / | 2| \-1 + cos(x)/ |
\ \ (-1 + cos(x)) / \ (-1 + cos(x)) / \ (-1 + cos(x)) / \ (-1 + cos(x)) / \ (-1 + cos(x)) / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 \
| (1 + sin(x)) | / 1 + sin(x)\
|1 + --------------|*(-1 + cos(x))*atan|-----------|
| 2| \-1 + cos(x)/
\ (-1 + cos(x)) /
$$\frac{2 \left(\left(- \frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{6 \left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + \frac{6 \left(\sin{\left(x \right)} + 1\right) \sin^{3}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{3}} - \cos{\left(x \right)} - \frac{3 \sin^{2}{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{3 \cos^{2}{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{6 \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}}\right) \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)} - \frac{4 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} + 1\right) \left(\frac{\left(\sin{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{2 \left(\sin{\left(x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \sin{\left(x \right)} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} - 1}\right) \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right)^{2}} - \frac{3 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right) \left(\frac{\left(\sin{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{2 \left(\sin{\left(x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \sin{\left(x \right)} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} - 1}\right) \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right) \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}} + \frac{3 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right) \left(\frac{\left(\sin{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{2 \left(\sin{\left(x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \sin{\left(x \right)} + \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} - 1}\right)}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right) \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}} - \frac{2 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right) \left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2} \cos{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{3 \left(\sin{\left(x \right)} + 1\right)^{2} \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)} + \frac{4 \left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos^{2}{\left(x \right)}\right) \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right)^{2}} + \frac{8 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{3} \left(\sin{\left(x \right)} + 1\right)^{2} \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right)^{2} \left(\cos{\left(x \right)} - 1\right)^{4}} + \frac{6 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{3} \left(\sin{\left(x \right)} + 1\right) \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right)^{2} \left(\cos{\left(x \right)} - 1\right)^{3} \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}} - \frac{6 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{3} \left(\sin{\left(x \right)} + 1\right)}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right)^{2} \left(\cos{\left(x \right)} - 1\right)^{3} \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}} + \frac{2 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{3} \log{\left(- \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)} \right)}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right)^{2} \left(\cos{\left(x \right)} - 1\right)^{2} \operatorname{atan}^{2}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}} - \frac{3 \left(\frac{\left(\sin{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)} - 1} + \cos{\left(x \right)}\right)^{3}}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right)^{2} \left(\cos{\left(x \right)} - 1\right)^{2} \operatorname{atan}^{2}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}}\right)}{\left(\frac{\left(\sin{\left(x \right)} + 1\right)^{2}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + 1\right) \left(\cos{\left(x \right)} - 1\right) \operatorname{atan}{\left(\frac{\sin{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} \right)}}$$
Gráfico