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 (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- y=(ch3x)^(arcsin(3x))
- y es igual a (ch3x) en el grado (arc seno de (3x))
- y=(ch3x)(arcsin(3x))
- y=ch3xarcsin3x
- y=ch3x^arcsin3x
Derivada de y=(ch3x)^(arcsin(3x))
Solución
Ha introducido
[src]
asin(3*x) cosh (3*x)
$$\cosh^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
cosh(3*x)^asin(3*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
asin(3*x) /3*log(cosh(3*x)) 3*asin(3*x)*sinh(3*x)\
cosh (3*x)*|---------------- + ---------------------|
| __________ cosh(3*x) |
| / 2 |
\ \/ 1 - 9*x /
$$\left(\frac{3 \sinh{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh{\left(3 x \right)}} + \frac{3 \log{\left(\cosh{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \cosh^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
Segunda derivada
[src]
/ 2 2 \
asin(3*x) |/log(cosh(3*x)) asin(3*x)*sinh(3*x)\ sinh (3*x)*asin(3*x) 2*sinh(3*x) 3*x*log(cosh(3*x)) |
9*cosh (3*x)*||-------------- + -------------------| - -------------------- + ----------------------- + ------------------ + asin(3*x)|
|| __________ cosh(3*x) | 2 __________ 3/2 |
|| / 2 | cosh (3*x) / 2 / 2\ |
\\\/ 1 - 9*x / \/ 1 - 9*x *cosh(3*x) \1 - 9*x / /
$$9 \left(\frac{3 x \log{\left(\cosh{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\sinh{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh{\left(3 x \right)}} + \frac{\log{\left(\cosh{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{2} - \frac{\sinh^{2}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh^{2}{\left(3 x \right)}} + \operatorname{asin}{\left(3 x \right)} + \frac{2 \sinh{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cosh{\left(3 x \right)}}\right) \cosh^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 3 2 \
asin(3*x) |/log(cosh(3*x)) asin(3*x)*sinh(3*x)\ 3 log(cosh(3*x)) /log(cosh(3*x)) asin(3*x)*sinh(3*x)\ | sinh (3*x)*asin(3*x) 2*sinh(3*x) 3*x*log(cosh(3*x)) | 3*sinh (3*x) 2*asin(3*x)*sinh(3*x) 2*sinh (3*x)*asin(3*x) 27*x *log(cosh(3*x)) 9*x*sinh(3*x) |
27*cosh (3*x)*||-------------- + -------------------| + ------------- + -------------- + 3*|-------------- + -------------------|*|- -------------------- + ----------------------- + ------------------ + asin(3*x)| - ------------------------ - --------------------- + ---------------------- + -------------------- + -----------------------|
|| __________ cosh(3*x) | __________ 3/2 | __________ cosh(3*x) | | 2 __________ 3/2 | __________ cosh(3*x) 3 5/2 3/2 |
|| / 2 | / 2 / 2\ | / 2 | | cosh (3*x) / 2 / 2\ | / 2 2 cosh (3*x) / 2\ / 2\ |
\\\/ 1 - 9*x / \/ 1 - 9*x \1 - 9*x / \\/ 1 - 9*x / \ \/ 1 - 9*x *cosh(3*x) \1 - 9*x / / \/ 1 - 9*x *cosh (3*x) \1 - 9*x / \1 - 9*x / *cosh(3*x)/
$$27 \left(\frac{27 x^{2} \log{\left(\cosh{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \frac{9 x \sinh{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \cosh{\left(3 x \right)}} + \left(\frac{\sinh{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh{\left(3 x \right)}} + \frac{\log{\left(\cosh{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right)^{3} + 3 \left(\frac{\sinh{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh{\left(3 x \right)}} + \frac{\log{\left(\cosh{\left(3 x \right)} \right)}}{\sqrt{1 - 9 x^{2}}}\right) \left(\frac{3 x \log{\left(\cosh{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} - \frac{\sinh^{2}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh^{2}{\left(3 x \right)}} + \operatorname{asin}{\left(3 x \right)} + \frac{2 \sinh{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cosh{\left(3 x \right)}}\right) + \frac{2 \sinh^{3}{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh^{3}{\left(3 x \right)}} - \frac{2 \sinh{\left(3 x \right)} \operatorname{asin}{\left(3 x \right)}}{\cosh{\left(3 x \right)}} - \frac{3 \sinh^{2}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \cosh^{2}{\left(3 x \right)}} + \frac{3}{\sqrt{1 - 9 x^{2}}} + \frac{\log{\left(\cosh{\left(3 x \right)} \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) \cosh^{\operatorname{asin}{\left(3 x \right)}}{\left(3 x \right)}$$
Gráfico