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 -5*tan(2*t)-4*cot(4*t)
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Derivada de (3x+6)^2
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Derivada de 3^(x*x)
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Derivada de 2*y-4
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Expresiones idénticas
- y=(sinh(x)^ dos +cosh(x)^ dos)^(x^ dos + tres)
- y es igual a ( seno hiperbólico de (x) al cuadrado más coseno de eno hiperbólico de (x) al cuadrado ) en el grado (x al cuadrado más 3)
- y es igual a ( seno hiperbólico de (x) en el grado dos más coseno de eno hiperbólico de (x) en el grado dos) en el grado (x en el grado dos más tres)
- y=(sinh(x)2+cosh(x)2)(x2+3)
- y=sinhx2+coshx2x2+3
- y=(sinh(x)²+cosh(x)²)^(x²+3)
- y=(sinh(x) en el grado 2+cosh(x) en el grado 2) en el grado (x en el grado 2+3)
- y=sinhx^2+coshx^2^x^2+3
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Expresiones semejantes
- y=(sinh(x)^2-cosh(x)^2)^(x^2+3)
- y=(sinh(x)^2+cosh(x)^2)^(x^2-3)
Derivada de y=(sinh(x)^2+cosh(x)^2)^(x^2+3)
Solución
Ha introducido
[src]
2
x + 3
/ 2 2 \
\sinh (x) + cosh (x)/
$$\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right)^{x^{2} + 3}$$
(sinh(x)^2 + cosh(x)^2)^(x^2 + 3)
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
x + 3 / / 2 \ \
/ 2 2 \ | / 2 2 \ 4*\x + 3/*cosh(x)*sinh(x)|
\sinh (x) + cosh (x)/ *|2*x*log\sinh (x) + cosh (x)/ + --------------------------|
| 2 2 |
\ sinh (x) + cosh (x) /
$$\left(2 x \log{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)} \right)} + \frac{4 \left(x^{2} + 3\right) \sinh{\left(x \right)} \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}\right) \left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right)^{x^{2} + 3}$$
Segunda derivada
[src]
2 / 2 \
3 + x | / / 2\ \ 2 / 2\ 2 / 2\ 2 2 / 2\ |
/ 2 2 \ | | / 2 2 \ 2*\3 + x /*cosh(x)*sinh(x)| 2*cosh (x)*\3 + x / 2*sinh (x)*\3 + x / 8*cosh (x)*sinh (x)*\3 + x / 8*x*cosh(x)*sinh(x) / 2 2 \|
2*\cosh (x) + sinh (x)/ *|2*|x*log\cosh (x) + sinh (x)/ + --------------------------| + ------------------- + ------------------- - ---------------------------- + ------------------- + log\cosh (x) + sinh (x)/|
| | 2 2 | 2 2 2 2 2 2 2 |
| \ cosh (x) + sinh (x) / cosh (x) + sinh (x) cosh (x) + sinh (x) / 2 2 \ cosh (x) + sinh (x) |
\ \cosh (x) + sinh (x)/ /
$$2 \left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right)^{x^{2} + 3} \left(\frac{8 x \sinh{\left(x \right)} \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} + \frac{2 \left(x^{2} + 3\right) \sinh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} + \frac{2 \left(x^{2} + 3\right) \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} - \frac{8 \left(x^{2} + 3\right) \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right)^{2}} + 2 \left(x \log{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)} \right)} + \frac{2 \left(x^{2} + 3\right) \sinh{\left(x \right)} \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}\right)^{2} + \log{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)} \right)}\right)$$
Tercera derivada
[src]
/ / 2 2 3 / 2\ 3 / 2\ 3 3 / 2\\ \
| | 2 2 / 2\ 12*x*cosh (x)*sinh (x) 6*cosh (x)*\3 + x /*sinh(x) 6*sinh (x)*\3 + x /*cosh(x) 16*cosh (x)*sinh (x)*\3 + x /| |
| 2*|3*x*cosh (x) + 3*x*sinh (x) + 3*cosh(x)*sinh(x) + 2*\3 + x /*cosh(x)*sinh(x) - ---------------------- - --------------------------- - --------------------------- + -----------------------------| |
2 | 3 | 2 2 2 2 2 2 2 | |
3 + x | / / 2\ \ | cosh (x) + sinh (x) cosh (x) + sinh (x) cosh (x) + sinh (x) / 2 2 \ | / / 2\ \ / 2 / 2\ 2 / 2\ 2 2 / 2\ \|
/ 2 2 \ | | / 2 2 \ 2*\3 + x /*cosh(x)*sinh(x)| \ \cosh (x) + sinh (x)/ / | / 2 2 \ 2*\3 + x /*cosh(x)*sinh(x)| |2*cosh (x)*\3 + x / 2*sinh (x)*\3 + x / 8*cosh (x)*sinh (x)*\3 + x / 8*x*cosh(x)*sinh(x) / 2 2 \||
4*\cosh (x) + sinh (x)/ *|2*|x*log\cosh (x) + sinh (x)/ + --------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 3*|x*log\cosh (x) + sinh (x)/ + --------------------------|*|------------------- + ------------------- - ---------------------------- + ------------------- + log\cosh (x) + sinh (x)/||
| | 2 2 | 2 2 | 2 2 | | 2 2 2 2 2 2 2 ||
| \ cosh (x) + sinh (x) / cosh (x) + sinh (x) \ cosh (x) + sinh (x) / |cosh (x) + sinh (x) cosh (x) + sinh (x) / 2 2 \ cosh (x) + sinh (x) ||
\ \ \cosh (x) + sinh (x)/ //
$$4 \left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right)^{x^{2} + 3} \left(2 \left(x \log{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)} \right)} + \frac{2 \left(x^{2} + 3\right) \sinh{\left(x \right)} \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}\right)^{3} + 3 \left(x \log{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)} \right)} + \frac{2 \left(x^{2} + 3\right) \sinh{\left(x \right)} \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}\right) \left(\frac{8 x \sinh{\left(x \right)} \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} + \frac{2 \left(x^{2} + 3\right) \sinh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} + \frac{2 \left(x^{2} + 3\right) \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} - \frac{8 \left(x^{2} + 3\right) \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right)^{2}} + \log{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)} \right)}\right) + \frac{2 \left(3 x \sinh^{2}{\left(x \right)} + 3 x \cosh^{2}{\left(x \right)} - \frac{12 x \sinh^{2}{\left(x \right)} \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} + 2 \left(x^{2} + 3\right) \sinh{\left(x \right)} \cosh{\left(x \right)} - \frac{6 \left(x^{2} + 3\right) \sinh^{3}{\left(x \right)} \cosh{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} - \frac{6 \left(x^{2} + 3\right) \sinh{\left(x \right)} \cosh^{3}{\left(x \right)}}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}} + \frac{16 \left(x^{2} + 3\right) \sinh^{3}{\left(x \right)} \cosh^{3}{\left(x \right)}}{\left(\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}\right)^{2}} + 3 \sinh{\left(x \right)} \cosh{\left(x \right)}\right)}{\sinh^{2}{\left(x \right)} + \cosh^{2}{\left(x \right)}}\right)$$