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 3*x*cos(x)-4*sin(x)
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Derivada de (3/x-4)*(3*x+6)
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Derivada de (-3+x³)(-4x³+3)
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Derivada de (3x)^(-3/2)
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Expresiones idénticas
- ((x-tgx^ uno / dos)/(x+tgx^ uno / dos))^ dos
- ((x menos tgx en el grado 1 dividir por 2) dividir por (x más tgx en el grado 1 dividir por 2)) al cuadrado
- ((x menos tgx en el grado uno dividir por dos) dividir por (x más tgx en el grado uno dividir por dos)) en el grado dos
- ((x-tgx1/2)/(x+tgx1/2))2
- x-tgx1/2/x+tgx1/22
- ((x-tgx^1/2)/(x+tgx^1/2))²
- ((x-tgx en el grado 1/2)/(x+tgx en el grado 1/2)) en el grado 2
- x-tgx^1/2/x+tgx^1/2^2
- ((x-tgx^1 dividir por 2) dividir por (x+tgx^1 dividir por 2))^2
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Expresiones semejantes
- ((x-tgx^1/2)/(x-tgx^1/2))^2
- ((x+tgx^1/2)/(x+tgx^1/2))^2
Derivada de ((x-tgx^1/2)/(x+tgx^1/2))^2
Solución
Ha introducido
[src]
2 / ________\ |x - \/ tan(x) | |--------------| | ________| \x + \/ tan(x) /
$$\left(\frac{x - \sqrt{\tan{\left(x \right)}}}{x + \sqrt{\tan{\left(x \right)}}}\right)^{2}$$
((x - sqrt(tan(x)))/(x + sqrt(tan(x))))^2
Solución detallada
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Sustituimos .
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Según el principio, aplicamos: tenemos
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Luego se aplica una cadena de reglas. Multiplicamos por :
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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diferenciamos miembro por miembro:
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Según el principio, aplicamos: tenemos
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La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
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Sustituimos .
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Según el principio, aplicamos: tenemos
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Luego se aplica una cadena de reglas. Multiplicamos por :
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Reescribimos las funciones para diferenciar:
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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La derivada del seno es igual al coseno:
Para calcular :
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La derivada del coseno es igual a menos el seno:
Ahora aplicamos la regla de la derivada de una divesión:
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Como resultado de la secuencia de reglas:
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Entonces, como resultado:
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Como resultado de:
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Para calcular :
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diferenciamos miembro por miembro:
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Según el principio, aplicamos: tenemos
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Sustituimos .
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Según el principio, aplicamos: tenemos
-
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Luego se aplica una cadena de reglas. Multiplicamos por :
Como resultado de la secuencia de reglas:
Como resultado de:
Ahora aplicamos la regla de la derivada de una divesión:
Como resultado de la secuencia de reglas:
Simplificamos:
Respuesta:
Primera derivada
[src]
/ / 2 \ / 2 \ \
| | 1 tan (x)| | 1 tan (x)| |
| | - + -------| | - + -------| |
| | 2 2 | | 2 2 | / ________\|
2 |2*|1 - -----------| 2*|-1 - -----------|*\x - \/ tan(x) /|
/ ________\ | | ________| | ________| |
\x - \/ tan(x) / / ________\ | \ \/ tan(x) / \ \/ tan(x) / |
-----------------*\x + \/ tan(x) /*|------------------- + -------------------------------------|
2 | ________ 2 |
/ ________\ | x + \/ tan(x) / ________\ |
\x + \/ tan(x) / \ \x + \/ tan(x) / /
------------------------------------------------------------------------------------------------
________
x - \/ tan(x)
$$\frac{\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right)^{2}}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}} \left(x + \sqrt{\tan{\left(x \right)}}\right) \left(\frac{2 \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(- \frac{\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}}{\sqrt{\tan{\left(x \right)}}} - 1\right)}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}} + \frac{2 \left(- \frac{\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}}{\sqrt{\tan{\left(x \right)}}} + 1\right)}{x + \sqrt{\tan{\left(x \right)}}}\right)}{x - \sqrt{\tan{\left(x \right)}}}$$
Segunda derivada
[src]
/ / 2 \ \
| | 1 + tan (x)| / ________\|
2 / 2 \ | |2 + -----------|*\x - \/ tan(x) /|
/ / 2 \ \ | / 2 \ / 2 \ / 2 \ / 2 \| / / 2 \ \ / 2 \ | 2 | ________| |
| | 1 + tan (x)| / ________\| | | 1 + tan (x)| / ________\ | 1 + tan (x)| | 1 + tan (x)| / 2 \ / ________\ | ________ 1 + tan (x)|| | | 1 + tan (x)| / ________\| | 1 + tan (x)| / ________\ | 1 + tan (x) \ \/ tan(x) / |
| |2 + -----------|*\x - \/ tan(x) /| | 2*|2 + -----------| *\x - \/ tan(x) / 2*|-2 + -----------|*|2 + -----------| \1 + tan (x)/*\x - \/ tan(x) /*|- 4*\/ tan(x) + -----------|| | |2 + -----------|*\x - \/ tan(x) /| |2 + -----------|*\x - \/ tan(x) /*|-2 + ----------- + ----------------------------------|
| 2 | ________| | | / 2 \ | ________| | ________| | ________| | 3/2 || / 2 \ | 2 | ________| | | ________| | ________ ________ |
| 1 + tan (x) \ \/ tan(x) / | / ________\ |/ 2 \ | ________ 1 + tan (x)| \ \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) / \ tan (x) /| | 1 + tan (x)| | 1 + tan (x) \ \/ tan(x) / | \ \/ tan(x) / \ \/ tan(x) x + \/ tan(x) /
2*|-2 + ----------- + ----------------------------------| + \x - \/ tan(x) /*|\1 + tan (x)/*|- 4*\/ tan(x) + -----------| + ------------------------------------- + -------------------------------------- + -------------------------------------------------------------| - |-2 + -----------|*|-2 + ----------- + ----------------------------------| - ------------------------------------------------------------------------------------------
| ________ ________ | | | 3/2 | 2 ________ ________ | | ________| | ________ ________ | ________
\ \/ tan(x) x + \/ tan(x) / | \ tan (x) / / ________\ x + \/ tan(x) x + \/ tan(x) | \ \/ tan(x) / \ \/ tan(x) x + \/ tan(x) / x + \/ tan(x)
\ \x + \/ tan(x) / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ ________\
2*\x + \/ tan(x) /
$$\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{2 \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{2}}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}} + \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{2 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}}\right) - \frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)}{x + \sqrt{\tan{\left(x \right)}}} - \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) + 2 \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)^{2}}{2 \left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}}$$
Tercera derivada
[src]
/ 2 \
/ / 2 \ \ | / 2 \ 2 2 / 2 \ / 2 \ / 2 \ | 2 2
| | 1 + tan (x)| / ________\| | | 1 + tan (x)| / ________\ / ________\ / 2 \ | ________ 1 + tan (x)| | 1 + tan (x)| | 1 + tan (x)| / ________\| / / 2 \ \ / / 2 \ \ / / 2 \ \ / / 2 \ \ / / 2 \ \
| |2 + -----------|*\x - \/ tan(x) /| | 2 3*|2 + -----------| *\x - \/ tan(x) / \x - \/ tan(x) / *\1 + tan (x)/*|- 4*\/ tan(x) + -----------| 4*|-2 + -----------|*|2 + -----------|*\x - \/ tan(x) /| | | 1 + tan (x)| / ________\| | | 1 + tan (x)| / ________\| | | 1 + tan (x)| / ________\| | | 1 + tan (x)| / ________\| | | 1 + tan (x)| / ________\|
/ 2 3 / 2\ \ / 2 \ | 2 | ________| | |/ 2 \ / 2 \ | ________| | 3/2 | | ________| | ________| | | |2 + -----------|*\x - \/ tan(x) /| | |2 + -----------|*\x - \/ tan(x) /| 2 | |2 + -----------|*\x - \/ tan(x) /| | |2 + -----------|*\x - \/ tan(x) /| | |2 + -----------|*\x - \/ tan(x) /|
| / 2 \ / 2 \ / 2 \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \| / / 2 \ \ | / 2 \ / 2 \ / 2 \ / 2 \| / / 2 \ \ | 1 + tan (x) \ \/ tan(x) / | || 1 + tan (x)| / 2 \ / ________\ | ________ 1 + tan (x)| \ \/ tan(x) / \ tan (x) / \ \/ tan(x) / \ \/ tan(x) / | | 2 | ________| | / 2 \ | 2 | ________| | / 2 \ / 2 \ | 2 | ________| | / 2 \ / 2 \ | 2 | ________| | / 2 \ | 2 | ________| |
| | 1 + tan (x)| | 1 + tan (x)| | 1 + tan (x)| / ________\ / 2 \ / ________\ | 3/2 4*\1 + tan (x)/ 3*\1 + tan (x)/ | / 2 \ | 1 + tan (x)| | ________ 1 + tan (x)| / 2 \ | 1 + tan (x)| | ________ 1 + tan (x)| / 2 \ | 1 + tan (x)| / ________\ | ________ 1 + tan (x)|| | | 1 + tan (x)| / ________\| | | 1 + tan (x)| / ________\ | 1 + tan (x)| | 1 + tan (x)| / 2 \ / ________\ | ________ 1 + tan (x)|| | | 1 + tan (x)| / ________\| 2*|-2 + ----------- + ----------------------------------|*||-2 + -----------| + \1 + tan (x)/*\x - \/ tan(x) /*|- 4*\/ tan(x) + -----------| + -------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------| | 1 + tan (x) \ \/ tan(x) / | | 1 + tan (x)| | 1 + tan (x) \ \/ tan(x) / | | 1 + tan (x)| | 1 + tan (x)| / ________\ | 1 + tan (x) \ \/ tan(x) / | | 1 + tan (x)| | 1 + tan (x)| | 1 + tan (x) \ \/ tan(x) / | / 2 \ / ________\ | ________ 1 + tan (x)| | 1 + tan (x) \ \/ tan(x) / |
| / 2\ 6*|2 + -----------| *|-2 + -----------| 6*|2 + -----------| *\x - \/ tan(x) / \1 + tan (x)/*\x - \/ tan(x) /*|16*tan (x) - --------------- + ----------------| 3*\1 + tan (x)/*|-2 + -----------|*|- 4*\/ tan(x) + -----------| 3*\1 + tan (x)/*|2 + -----------|*|- 4*\/ tan(x) + -----------| 6*\1 + tan (x)/*|2 + -----------|*\x - \/ tan(x) /*|- 4*\/ tan(x) + -----------|| | |2 + -----------|*\x - \/ tan(x) /| | 2*|2 + -----------| *\x - \/ tan(x) / 2*|-2 + -----------|*|2 + -----------| \1 + tan (x)/*\x - \/ tan(x) /*|- 4*\/ tan(x) + -----------|| | |2 + -----------|*\x - \/ tan(x) /| | ________ ________ | || ________| | 3/2 | 2 ________ ________ | 2*|-2 + ----------- + ----------------------------------| *|2 + -----------| 2*|-2 + ----------- + ----------------------------------| *|-2 + -----------| 2*|2 + -----------| *\x - \/ tan(x) /*|-2 + ----------- + ----------------------------------| 2*|-2 + -----------|*|2 + -----------|*|-2 + ----------- + ----------------------------------| \1 + tan (x)/*\x - \/ tan(x) /*|- 4*\/ tan(x) + -----------|*|-2 + ----------- + ----------------------------------|
| | / 2 \ / 2 \ | | ________| | ________| | ________| | ________ 5/2 | | ________| | 3/2 | | ________| | 3/2 | | ________| | 3/2 || | 2 | ________| | | / 2 \ | ________| | ________| | ________| | 3/2 || / 2 \ | 2 | ________| | \ \/ tan(x) x + \/ tan(x) / |\ \/ tan(x) / \ tan (x) / / ________\ x + \/ tan(x) x + \/ tan(x) | | ________ ________ | | ________| | ________ ________ | | ________| | ________| | ________ ________ | | ________| | ________| | ________ ________ | | 3/2 | | ________ ________ |
/ ________\ |/ 2 \ | 3/2 4*\1 + tan (x)/ 3*\1 + tan (x)/ | \ \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) tan (x) / \ \/ tan(x) / \ tan (x) / \ \/ tan(x) / \ tan (x) / \ \/ tan(x) / \ tan (x) /| | 1 + tan (x) \ \/ tan(x) / | |/ 2 \ | ________ 1 + tan (x)| \ \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) / \ tan (x) /| / 2 \ | ________ 1 + tan (x)| | 1 + tan (x) \ \/ tan(x) / | \ \x + \/ tan(x) / / \ \/ tan(x) x + \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) x + \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) x + \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) / \ \/ tan(x) x + \/ tan(x) / \ tan (x) / \ \/ tan(x) x + \/ tan(x) /
- \x - \/ tan(x) /*|\1 + tan (x)/*|16*tan (x) - --------------- + ----------------| + --------------------------------------- + ------------------------------------- + ---------------------------------------------------------------------------------- + ----------------------------------------------------------------- + ---------------------------------------------------------------- + ---------------------------------------------------------------------------------| - 2*|-2 + ----------- + ----------------------------------|*|\1 + tan (x)/*|- 4*\/ tan(x) + -----------| + ------------------------------------- + -------------------------------------- + -------------------------------------------------------------| + \1 + tan (x)/*|- 4*\/ tan(x) + -----------|*|-2 + ----------- + ----------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------
| | ________ 5/2 | 2 3 ________ ________ ________ 2 | | ________ ________ | | | 3/2 | 2 ________ ________ | | 3/2 | | ________ ________ | ________ ________ ________ 2 ________ ________
| \ \/ tan(x) tan (x) / / ________\ / ________\ x + \/ tan(x) x + \/ tan(x) x + \/ tan(x) / ________\ | \ \/ tan(x) x + \/ tan(x) / | \ tan (x) / / ________\ x + \/ tan(x) x + \/ tan(x) | \ tan (x) / \ \/ tan(x) x + \/ tan(x) / x - \/ tan(x) x + \/ tan(x) x - \/ tan(x) / ________\ x + \/ tan(x) x + \/ tan(x)
\ \x + \/ tan(x) / \x + \/ tan(x) / \x + \/ tan(x) / / \ \x + \/ tan(x) / / \x + \/ tan(x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ ________\
4*\x + \/ tan(x) /
$$\frac{- \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 16 \tan^{\frac{3}{2}}{\left(x \right)}\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{6 \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}} + \frac{6 \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{3}}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{3}} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 16 \tan^{\frac{3}{2}}{\left(x \right)}\right) + \frac{3 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{3 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{6 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{2}}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}}\right) + \frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{2 \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{2} \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}} + \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) - 2 \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{2 \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{2}}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}} + \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{2 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}}\right) + \frac{2 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{2 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)^{2}}{x + \sqrt{\tan{\left(x \right)}}} + \frac{2 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)^{2}}{x - \sqrt{\tan{\left(x \right)}}} - \frac{2 \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\left(x - \sqrt{\tan{\left(x \right)}}\right)^{2} \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x + \sqrt{\tan{\left(x \right)}}} + \frac{3 \left(x - \sqrt{\tan{\left(x \right)}}\right)^{2} \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{2}}{\left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}} + \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{4 \left(x - \sqrt{\tan{\left(x \right)}}\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} + 2\right)}{x + \sqrt{\tan{\left(x \right)}}} + \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{\tan{\left(x \right)}}} - 2\right)^{2}\right)}{x - \sqrt{\tan{\left(x \right)}}}}{4 \left(x + \sqrt{\tan{\left(x \right)}}\right)^{2}}$$
Gráfico