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/x^5
-
Derivada de x*e^(-x^2)
-
Derivada de 1/(x+1)^2
-
Derivada de x^(4/5)
-
Expresiones idénticas
- y=(tg(dos x))^(ctg(x/2))
- y es igual a (tg(2x)) en el grado (ctg(x dividir por 2))
- y es igual a (tg(dos x)) en el grado (ctg(x dividir por 2))
- y=(tg(2x))(ctg(x/2))
- y=tg2xctgx/2
- y=tg2x^ctgx/2
- y=(tg(2x))^(ctg(x dividir por 2))
-
Expresiones con funciones
- tg
- tgx-ctgx
- tg^3(2x)
- tg5x^1/5
- tg^2(3x)
- tg(cosx)
- ctg
- ctg(x^2)
- ctg(x/7)
- ctg(2x+1)
Derivada de y=(tg(2x))^(ctg(x/2))
Solución
Ha introducido
[src]
/x\
cot|-|
\2/
(tan(2*x))
$$\tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
tan(2*x)^cot(x/2)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
-
Simplificamos:
Respuesta:
Primera derivada
[src]
/x\ // 2/x\\ / 2 \ /x\\
cot|-| || cot |-|| \2 + 2*tan (2*x)/*cot|-||
\2/ || 1 \2/| \2/|
(tan(2*x)) *||- - - -------|*log(tan(2*x)) + ------------------------|
\\ 2 2 / tan(2*x) /
$$\left(\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} + \left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} - \frac{1}{2}\right) \log{\left(\tan{\left(2 x \right)} \right)}\right) \tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
Segunda derivada
[src]
/ 2 \
|/ / 2 \ /x\\ |
|| 4*\1 + tan (2*x)/*cot|-|| 2 |
/x\ || / 2/x\\ \2/| / 2/x\\ /x\ / 2 \ /x\ / 2/x\\ / 2 \|
cot|-| ||- |1 + cot |-||*log(tan(2*x)) + ------------------------| |1 + cot |-||*cot|-|*log(tan(2*x)) 4*\1 + tan (2*x)/ *cot|-| 2*|1 + cot |-||*\1 + tan (2*x)/|
\2/ |\ \ \2// tan(2*x) / / 2 \ /x\ \ \2// \2/ \2/ \ \2// |
(tan(2*x)) *|----------------------------------------------------------- + 8*\1 + tan (2*x)/*cot|-| + ---------------------------------- - ------------------------- - -------------------------------|
| 4 \2/ 2 2 tan(2*x) |
\ tan (2*x) /
$$\left(\frac{\left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right)^{2}}{4} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(2 x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot{\left(\frac{x}{2} \right)}}{2}\right) \tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
Tercera derivada
[src]
/ / 2 \ \
| 3 / / 2 \ /x\\ | / 2/x\\ / 2 \ / 2 \ /x\| |
|/ / 2 \ /x\\ | 4*\1 + tan (2*x)/*cot|-|| | 4*|1 + cot |-||*\1 + tan (2*x)/ 8*\1 + tan (2*x)/ *cot|-|| |
|| 4*\1 + tan (2*x)/*cot|-|| | / 2/x\\ \2/| | / 2 \ /x\ / 2/x\\ /x\ \ \2// \2/| 2 2 2 3 |
/x\ || / 2/x\\ \2/| 3*|- |1 + cot |-||*log(tan(2*x)) + ------------------------|*|- 16*\1 + tan (2*x)/*cot|-| - |1 + cot |-||*cot|-|*log(tan(2*x)) + ------------------------------- + -------------------------| / 2/x\\ / 2 \ /x\ / 2 \ / 2/x\\ / 2 \ /x\ 2/x\ / 2/x\\ / 2/x\\ / 2 \ /x\|
cot|-| ||- |1 + cot |-||*log(tan(2*x)) + ------------------------| \ \ \2// tan(2*x) / | \2/ \ \2// \2/ tan(2*x) 2 | |1 + cot |-|| *log(tan(2*x)) 32*\1 + tan (2*x)/ *cot|-| 6*\1 + tan (2*x)/ *|1 + cot |-|| 16*\1 + tan (2*x)/ *cot|-| cot |-|*|1 + cot |-||*log(tan(2*x)) 3*|1 + cot |-||*\1 + tan (2*x)/*cot|-||
\2/ |\ \ \2// tan(2*x) / / 2/x\\ / 2 \ \ tan (2*x) / \ \2// \2/ \ \2// \2/ / 2 \ /x\ \2/ \ \2// \ \2// \2/|
(tan(2*x)) *|----------------------------------------------------------- - 12*|1 + cot |-||*\1 + tan (2*x)/ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------- - -------------------------- + -------------------------------- + -------------------------- + 32*\1 + tan (2*x)/*cot|-|*tan(2*x) - ----------------------------------- + --------------------------------------|
| 8 \ \2// 4 4 tan(2*x) 2 3 \2/ 2 tan(2*x) |
\ tan (2*x) tan (2*x) /
$$\left(\frac{\left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right)^{3}}{8} - \frac{3 \left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right) \left(\frac{8 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(2 x \right)}} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(2 x \right)}} - 16 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot{\left(\frac{x}{2} \right)}\right)}{4} + \frac{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \cot{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(2 x \right)}} + \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan^{2}{\left(2 x \right)}} - \frac{32 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - 12 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) + \frac{3 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} \cot{\left(\frac{x}{2} \right)} - \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \log{\left(\tan{\left(2 x \right)} \right)}}{4} - \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot^{2}{\left(\frac{x}{2} \right)}}{2}\right) \tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
Gráfico