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 1/(x+1)^2
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Derivada de (x+3)/(x-2)
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Derivada de (x+4)^2*(x+1)+9
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Derivada de e^(2-x)
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Expresiones idénticas
- y=sinh^- uno (tanh(x))
- y es igual a seno hiperbólico de en el grado menos 1( tangente de gente hiperbólica de (x))
- y es igual a seno hiperbólico de en el grado menos uno ( tangente de gente hiperbólica de (x))
- y=sinh-1(tanh(x))
- y=sinh-1tanhx
- y=sinh^-1tanhx
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Expresiones semejantes
- y=sinh^+1(tanh(x))
Derivada de y=sinh^-1(tanh(x))
Solución
Ha introducido
[src]
1 ------------- sinh(tanh(x))
$$\frac{1}{\sinh{\left(\tanh{\left(x \right)} \right)}}$$
1/sinh(tanh(x))
Primera derivada
[src]
/ 2 \
-\1 - tanh (x)/*cosh(tanh(x))
------------------------------
2
sinh (tanh(x))
$$- \frac{\left(1 - \tanh^{2}{\left(x \right)}\right) \cosh{\left(\tanh{\left(x \right)} \right)}}{\sinh^{2}{\left(\tanh{\left(x \right)} \right)}}$$
Segunda derivada
[src]
/ 2 / 2 \\
/ 2 \ | 2 2*cosh(tanh(x))*tanh(x) 2*cosh (tanh(x))*\-1 + tanh (x)/|
\-1 + tanh (x)/*|1 - tanh (x) - ----------------------- + --------------------------------|
| sinh(tanh(x)) 2 |
\ sinh (tanh(x)) /
-------------------------------------------------------------------------------------------
sinh(tanh(x))
$$\frac{\left(\tanh^{2}{\left(x \right)} - 1\right) \left(\frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right) \cosh^{2}{\left(\tanh{\left(x \right)} \right)}}{\sinh^{2}{\left(\tanh{\left(x \right)} \right)}} - \tanh^{2}{\left(x \right)} + 1 - \frac{2 \cosh{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}}\right)}{\sinh{\left(\tanh{\left(x \right)} \right)}}$$
Tercera derivada
[src]
/ 2 2 \
| / 2 \ / 2 \ 2 / 2 \ 3 2 / 2 \ |
/ 2 \ | / 2 \ 5*\-1 + tanh (x)/ *cosh(tanh(x)) 2*\-1 + tanh (x)/*cosh(tanh(x)) 4*tanh (x)*cosh(tanh(x)) 6*\-1 + tanh (x)/ *cosh (tanh(x)) 12*cosh (tanh(x))*\-1 + tanh (x)/*tanh(x)|
\-1 + tanh (x)/*|6*\-1 + tanh (x)/*tanh(x) - -------------------------------- + ------------------------------- + ------------------------ + --------------------------------- - -----------------------------------------|
| sinh(tanh(x)) sinh(tanh(x)) sinh(tanh(x)) 3 2 |
\ sinh (tanh(x)) sinh (tanh(x)) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
sinh(tanh(x))
$$\frac{\left(\tanh^{2}{\left(x \right)} - 1\right) \left(- \frac{5 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \cosh{\left(\tanh{\left(x \right)} \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}} + \frac{6 \left(\tanh^{2}{\left(x \right)} - 1\right)^{2} \cosh^{3}{\left(\tanh{\left(x \right)} \right)}}{\sinh^{3}{\left(\tanh{\left(x \right)} \right)}} + 6 \left(\tanh^{2}{\left(x \right)} - 1\right) \tanh{\left(x \right)} + \frac{2 \left(\tanh^{2}{\left(x \right)} - 1\right) \cosh{\left(\tanh{\left(x \right)} \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}} - \frac{12 \left(\tanh^{2}{\left(x \right)} - 1\right) \cosh^{2}{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{\sinh^{2}{\left(\tanh{\left(x \right)} \right)}} + \frac{4 \cosh{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{\sinh{\left(\tanh{\left(x \right)} \right)}}\right)}{\sinh{\left(\tanh{\left(x \right)} \right)}}$$
Gráfico