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 e^x*sin(x)
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Derivada de x*e^(1/x)
- Derivada de x!
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Derivada de e^y
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Expresiones idénticas
- y=(\sqrt(tgx))^(x+ uno)
- y es igual a (\ raíz cuadrada de (tgx)) en el grado (x más 1)
- y es igual a (\ raíz cuadrada de (tgx)) en el grado (x más uno)
- y=(\√(tgx))^(x+1)
- y=(\sqrt(tgx))(x+1)
- y=\sqrttgxx+1
- y=\sqrttgx^x+1
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Expresiones semejantes
- y=(\sqrt(tgx))^(x-1)
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x-1)/(sqrt(x^2)-x-1)
- sqrt(x)/(x+1)
- sqrt(x)+1
- sqrt(ln(x))
- sqrt(x)*cos^5*(3x)
- tgx
- tgx-ctgx
Derivada de y=(\sqrt(tgx))^(x+1)
Solución
Ha introducido
[src]
x + 1 ________ \/ tan(x)
$$\left(\sqrt{\tan{\left(x \right)}}\right)^{x + 1}$$
(sqrt(tan(x)))^(x + 1)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
// 2 \ \
1 x ||1 tan (x)| |
- + - ||- + -------|*(x + 1) |
2 2 |\2 2 / / ________\|
(tan(x)) *|--------------------- + log\\/ tan(x) /|
\ tan(x) /
$$\left(\frac{\left(x + 1\right) \left(\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}\right)}{\tan{\left(x \right)}} + \log{\left(\sqrt{\tan{\left(x \right)}} \right)}\right) \tan^{\frac{x}{2} + \frac{1}{2}}{\left(x \right)}$$
Segunda derivada
[src]
1 x
- + - // / 2 \\ / / 2 \ \ / / 2 \\\
2 2 || / ________\ (1 + x)*\1 + tan (x)/| |(1 + x)*\1 + tan (x)/ | / 2 \ | 2 (1 + x)*\1 + tan (x)/||
(tan(x)) *||2*log\\/ tan(x) / + ---------------------|*|--------------------- + log(tan(x))| + 2*\1 + tan (x)/*|2 + 2*x + ------ - ---------------------||
|\ tan(x) / \ tan(x) / | tan(x) 2 ||
\ \ tan (x) //
--------------------------------------------------------------------------------------------------------------------------------------------------------------
4
$$\frac{\left(\left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \log{\left(\sqrt{\tan{\left(x \right)}} \right)}\right) \left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 x - \frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 + \frac{2}{\tan{\left(x \right)}}\right)\right) \tan^{\frac{x}{2} + \frac{1}{2}}{\left(x \right)}}{4}$$
Tercera derivada
[src]
/ 2 / / 2 \ \ / / 2 \\ / / 2 \\ / / 2 \\\
| / / 2 \ \ / / 2 \\ / 2 \ |(1 + x)*\1 + tan (x)/ | | 2 (1 + x)*\1 + tan (x)/| / 2 \ | / ________\ (1 + x)*\1 + tan (x)/| | 2 (1 + x)*\1 + tan (x)/||
1 x | 2 |(1 + x)*\1 + tan (x)/ | | / ________\ (1 + x)*\1 + tan (x)/| 3 \1 + tan (x)/*|--------------------- + log(tan(x))|*|2 + 2*x + ------ - ---------------------| 2 \1 + tan (x)/*|2*log\\/ tan(x) / + ---------------------|*|2 + 2*x + ------ - ---------------------||
- + - | / 2 \ |--------------------- + log(tan(x))| *|2*log\\/ tan(x) / + ---------------------| / 2 \ \ tan(x) / | tan(x) 2 | / 2 \ \ tan(x) / | tan(x) 2 ||
2 2 | 2 3*\1 + tan (x)/ \ tan(x) / \ tan(x) / \1 + tan (x)/ *(1 + x) \ tan (x) / 2*\1 + tan (x)/ *(1 + x) / 2 \ \ tan (x) /|
(tan(x)) *|3 + 3*tan (x) - ---------------- + ---------------------------------------------------------------------------------- + ---------------------- + ---------------------------------------------------------------------------------------------- - ------------------------ + 2*(1 + x)*\1 + tan (x)/*tan(x) + ----------------------------------------------------------------------------------------------------|
| 2 8 3 2 tan(x) 4 |
\ 2*tan (x) tan (x) /
$$\left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{2 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 2 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \frac{\left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \log{\left(\sqrt{\tan{\left(x \right)}} \right)}\right) \left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{2}}{8} + \frac{\left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + 2 \log{\left(\sqrt{\tan{\left(x \right)}} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 x - \frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 + \frac{2}{\tan{\left(x \right)}}\right)}{4} + \frac{\left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 x - \frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 + \frac{2}{\tan{\left(x \right)}}\right)}{2} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{2 \tan^{2}{\left(x \right)}} + 3 \tan^{2}{\left(x \right)} + 3\right) \tan^{\frac{x}{2} + \frac{1}{2}}{\left(x \right)}$$
Gráfico