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 x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de (-2)/x^3
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Expresiones idénticas
- y=(ch*x)^arccos5x
- y es igual a (ch multiplicar por x) en el grado arc coseno de 5x
- y=(ch*x)arccos5x
- y=ch*xarccos5x
- y=(chx)^arccos5x
- y=(chx)arccos5x
- y=chxarccos5x
- y=chx^arccos5x
Derivada de y=(ch*x)^arccos5x
Solución
Ha introducido
[src]
acos(5*x) cosh (x)
$$\cosh^{\operatorname{acos}{\left(5 x \right)}}{\left(x \right)}$$
cosh(x)^acos(5*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
acos(5*x) / 5*log(cosh(x)) acos(5*x)*sinh(x)\
cosh (x)*|- -------------- + -----------------|
| ___________ cosh(x) |
| / 2 |
\ \/ 1 - 25*x /
$$\left(\frac{\sinh{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh{\left(x \right)}} - \frac{5 \log{\left(\cosh{\left(x \right)} \right)}}{\sqrt{1 - 25 x^{2}}}\right) \cosh^{\operatorname{acos}{\left(5 x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 2 \
acos(5*x) |/ 5*log(cosh(x)) acos(5*x)*sinh(x)\ sinh (x)*acos(5*x) 125*x*log(cosh(x)) 10*sinh(x) |
cosh (x)*||- -------------- + -----------------| - ------------------ - ------------------ - ---------------------- + acos(5*x)|
|| ___________ cosh(x) | 2 3/2 ___________ |
|| / 2 | cosh (x) / 2\ / 2 |
\\ \/ 1 - 25*x / \1 - 25*x / \/ 1 - 25*x *cosh(x) /
$$\left(- \frac{125 x \log{\left(\cosh{\left(x \right)} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\sinh{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh{\left(x \right)}} - \frac{5 \log{\left(\cosh{\left(x \right)} \right)}}{\sqrt{1 - 25 x^{2}}}\right)^{2} - \frac{\sinh^{2}{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh^{2}{\left(x \right)}} + \operatorname{acos}{\left(5 x \right)} - \frac{10 \sinh{\left(x \right)}}{\sqrt{1 - 25 x^{2}} \cosh{\left(x \right)}}\right) \cosh^{\operatorname{acos}{\left(5 x \right)}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 3 2 \
acos(5*x) |/ 5*log(cosh(x)) acos(5*x)*sinh(x)\ 15 125*log(cosh(x)) / 5*log(cosh(x)) acos(5*x)*sinh(x)\ | sinh (x)*acos(5*x) 10*sinh(x) 125*x*log(cosh(x))| 9375*x *log(cosh(x)) 2*acos(5*x)*sinh(x) 2*sinh (x)*acos(5*x) 15*sinh (x) 375*x*sinh(x) |
cosh (x)*||- -------------- + -----------------| - -------------- - ---------------- - 3*|- -------------- + -----------------|*|-acos(5*x) + ------------------ + ---------------------- + ------------------| - -------------------- - ------------------- + -------------------- + ----------------------- - ----------------------|
|| ___________ cosh(x) | ___________ 3/2 | ___________ cosh(x) | | 2 ___________ 3/2 | 5/2 cosh(x) 3 ___________ 3/2 |
|| / 2 | / 2 / 2\ | / 2 | | cosh (x) / 2 / 2\ | / 2\ cosh (x) / 2 2 / 2\ |
\\ \/ 1 - 25*x / \/ 1 - 25*x \1 - 25*x / \ \/ 1 - 25*x / \ \/ 1 - 25*x *cosh(x) \1 - 25*x / / \1 - 25*x / \/ 1 - 25*x *cosh (x) \1 - 25*x / *cosh(x)/
$$\left(- \frac{9375 x^{2} \log{\left(\cosh{\left(x \right)} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} - \frac{375 x \sinh{\left(x \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \cosh{\left(x \right)}} + \left(\frac{\sinh{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh{\left(x \right)}} - \frac{5 \log{\left(\cosh{\left(x \right)} \right)}}{\sqrt{1 - 25 x^{2}}}\right)^{3} - 3 \left(\frac{\sinh{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh{\left(x \right)}} - \frac{5 \log{\left(\cosh{\left(x \right)} \right)}}{\sqrt{1 - 25 x^{2}}}\right) \left(\frac{125 x \log{\left(\cosh{\left(x \right)} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + \frac{\sinh^{2}{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh^{2}{\left(x \right)}} - \operatorname{acos}{\left(5 x \right)} + \frac{10 \sinh{\left(x \right)}}{\sqrt{1 - 25 x^{2}} \cosh{\left(x \right)}}\right) + \frac{2 \sinh^{3}{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh^{3}{\left(x \right)}} - \frac{2 \sinh{\left(x \right)} \operatorname{acos}{\left(5 x \right)}}{\cosh{\left(x \right)}} + \frac{15 \sinh^{2}{\left(x \right)}}{\sqrt{1 - 25 x^{2}} \cosh^{2}{\left(x \right)}} - \frac{15}{\sqrt{1 - 25 x^{2}}} - \frac{125 \log{\left(\cosh{\left(x \right)} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}\right) \cosh^{\operatorname{acos}{\left(5 x \right)}}{\left(x \right)}$$
Gráfico