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^-1
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Derivada de (x^2)'
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Derivada de y
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Derivada de (x^5+1)
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Expresiones idénticas
- y=e^sinx^+secx
- y es igual a e en el grado seno de x en el grado más secx
- y=esinx+secx
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Expresiones semejantes
- y=e^sinx^-secx
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Expresiones con funciones
- sinx
- sinx+2cosx
- sinx*log5x
- sinx^sinx
- sinx/(2+cosx)
- sinx/(3-2cos(x))
- secx
- secx/tanx
Derivada de y=e^sinx^+secx
Solución
Ha introducido
[src]
sec(x) sin (x) E
$$e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}}$$
E^(sin(x)^sec(x))
Solución detallada
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Sustituimos .
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Derivado es.
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Luego se aplica una cadena de reglas. Multiplicamos por :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Como resultado de la secuencia de reglas:
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Respuesta:
Primera derivada
[src]
sec(x)
sec(x) /cos(x)*sec(x) \ sin (x)
sin (x)*|------------- + log(sin(x))*sec(x)*tan(x)|*e
\ sin(x) /
$$\left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} \sec{\left(x \right)} + \frac{\cos{\left(x \right)} \sec{\left(x \right)}}{\sin{\left(x \right)}}\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sin^{\sec{\left(x \right)}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 2 2 \ sec(x)
sec(x) | /cos(x) \ 2 / 2 \ cos (x) /cos(x) \ sec(x) 2*cos(x)*tan(x)| sin (x)
sin (x)*|-1 + |------ + log(sin(x))*tan(x)| *sec(x) + tan (x)*log(sin(x)) + \1 + tan (x)/*log(sin(x)) - ------- + |------ + log(sin(x))*tan(x)| *sin (x)*sec(x) + ---------------|*e *sec(x)
| \sin(x) / 2 \sin(x) / sin(x) |
\ sin (x) /
$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} \sec{\left(x \right)} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 1 + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)}$$
Tercera derivada
[src]
/ 3 3 3 2 3 2 / 2 \ / 2 \ / 2 \ \ sec(x)
sec(x) | /cos(x) \ 2 3 2*cos (x) 2*cos(x) /cos(x) \ 2 2*sec(x) 3*cos (x)*tan(x) /cos(x) \ 2 sec(x) 3*tan (x)*cos(x) 3*\1 + tan (x)/*cos(x) /cos(x) \ | 2 / 2 \ cos (x) 2*cos(x)*tan(x)| / 2 \ sec(x) /cos(x) \ | 2 / 2 \ cos (x) 2*cos(x)*tan(x)| | sin (x)
sin (x)*|-3*tan(x) + |------ + log(sin(x))*tan(x)| *sec (x) + tan (x)*log(sin(x)) + --------- + -------- + |------ + log(sin(x))*tan(x)| *sec (x)*sin (x) - ---------------- + 3*|------ + log(sin(x))*tan(x)| *sec (x)*sin (x) + ---------------- + ---------------------- + 3*|------ + log(sin(x))*tan(x)|*|-1 + tan (x)*log(sin(x)) + \1 + tan (x)/*log(sin(x)) - ------- + ---------------|*sec(x) + 5*\1 + tan (x)/*log(sin(x))*tan(x) + 3*sin (x)*|------ + log(sin(x))*tan(x)|*|-1 + tan (x)*log(sin(x)) + \1 + tan (x)/*log(sin(x)) - ------- + ---------------|*sec(x)|*e *sec(x)
| \sin(x) / 3 sin(x) \sin(x) / 2 \sin(x) / sin(x) sin(x) \sin(x) / | 2 sin(x) | \sin(x) / | 2 sin(x) | |
\ sin (x) sin (x) \ sin (x) / \ sin (x) / /
$$\left(\left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \sin^{2 \sec{\left(x \right)}}{\left(x \right)} \sec^{2}{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec^{2}{\left(x \right)} + \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} \sec^{2}{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 1 + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} + \log{\left(\sin{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - 1 + \frac{2 \cos{\left(x \right)} \tan{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \sec{\left(x \right)} + 5 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\sin{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(\sin{\left(x \right)} \right)} \tan^{3}{\left(x \right)} - 3 \tan{\left(x \right)} + \frac{3 \cos{\left(x \right)} \tan^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{3 \cos^{2}{\left(x \right)} \tan{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) e^{\sin^{\sec{\left(x \right)}}{\left(x \right)}} \sin^{\sec{\left(x \right)}}{\left(x \right)} \sec{\left(x \right)}$$
Gráfico