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^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- y=ex^√sinx
- y es igual a ex en el grado √ seno de x
- y=ex√sinx
Derivada de y=ex^√sinx
Solución
Ha introducido
[src]
/ ________\ | \/ sin(x) | \x / E
$$e^{x^{\sqrt{\sin{\left(x \right)}}}}$$
E^(x^(sqrt(sin(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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Simplificamos:
Respuesta:
Primera derivada
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/ ________\
________ / ________ \ | \/ sin(x) |
\/ sin(x) |\/ sin(x) cos(x)*log(x)| \x /
x *|---------- + -------------|*e
| x ________|
\ 2*\/ sin(x) /
$$x^{\sqrt{\sin{\left(x \right)}}} \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}} + \frac{\sqrt{\sin{\left(x \right)}}}{x}\right) e^{x^{\sqrt{\sin{\left(x \right)}}}}$$
Segunda derivada
[src]
/ 2 2 \
|/ ________ \ ________ / ________ \ |
||2*\/ sin(x) cos(x)*log(x)| \/ sin(x) |2*\/ sin(x) cos(x)*log(x)| |
||------------ + -------------| x *|------------ + -------------| | / ________\
________ || x ________ | ________ ________ | x ________ | 2 | | \/ sin(x) |
\/ sin(x) |\ \/ sin(x) / \/ sin(x) \/ sin(x) *log(x) \ \/ sin(x) / cos(x) cos (x)*log(x)| \x /
x *|------------------------------- - ---------- - ----------------- + ------------------------------------------- + ------------ - --------------|*e
| 4 2 2 4 ________ 3/2 |
\ x x*\/ sin(x) 4*sin (x) /
$$x^{\sqrt{\sin{\left(x \right)}}} \left(\frac{x^{\sqrt{\sin{\left(x \right)}}} \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x}\right)^{2}}{4} + \frac{\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x}\right)^{2}}{4} - \frac{\log{\left(x \right)} \sqrt{\sin{\left(x \right)}}}{2} - \frac{\log{\left(x \right)} \cos^{2}{\left(x \right)}}{4 \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{\cos{\left(x \right)}}{x \sqrt{\sin{\left(x \right)}}} - \frac{\sqrt{\sin{\left(x \right)}}}{x^{2}}\right) e^{x^{\sqrt{\sin{\left(x \right)}}}}$$
Tercera derivada
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/ 3 3 3 \
|/ ________ \ / ________ \ / ________ 2 \ ________ / ________ \ ________ / ________ \ ________ / ________ \ / ________ 2 \ |
||2*\/ sin(x) cos(x)*log(x)| |2*\/ sin(x) cos(x)*log(x)| | ________ 4*\/ sin(x) cos (x)*log(x) 4*cos(x) | 2*\/ sin(x) |2*\/ sin(x) cos(x)*log(x)| \/ sin(x) |2*\/ sin(x) cos(x)*log(x)| \/ sin(x) |2*\/ sin(x) cos(x)*log(x)| | ________ 4*\/ sin(x) cos (x)*log(x) 4*cos(x) | |
||------------ + -------------| 3*|------------ + -------------|*|2*\/ sin(x) *log(x) + ------------ + -------------- - ------------| x *|------------ + -------------| 3*x *|------------ + -------------| 3*x *|------------ + -------------|*|2*\/ sin(x) *log(x) + ------------ + -------------- - ------------| | / ________\
________ || x ________ | ________ ________ | x ________ | | 2 3/2 ________| | x ________ | | x ________ | 2 | x ________ | | 2 3/2 ________| 3 | | \/ sin(x) |
\/ sin(x) |\ \/ sin(x) / 2*\/ sin(x) 3*\/ sin(x) \ \/ sin(x) / \ x sin (x) x*\/ sin(x) / \ \/ sin(x) / \ \/ sin(x) / 3*cos(x) 3*cos (x) \ \/ sin(x) / \ x sin (x) x*\/ sin(x) / cos(x)*log(x) 3*cos (x)*log(x)| \x /
x *|------------------------------- + ------------ - ------------ - ----------------------------------------------------------------------------------------------------- + --------------------------------------------- + --------------------------------------------- - --------------- - ------------- - ----------------------------------------------------------------------------------------------------------------- + ------------- + ----------------|*e
| 8 3 2*x 8 8 8 2 ________ 3/2 8 ________ 5/2 |
\ x 2*x *\/ sin(x) 4*x*sin (x) 4*\/ sin(x) 8*sin (x) /
$$x^{\sqrt{\sin{\left(x \right)}}} \left(\frac{x^{2 \sqrt{\sin{\left(x \right)}}} \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x}\right)^{3}}{8} + \frac{3 x^{\sqrt{\sin{\left(x \right)}}} \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x}\right)^{3}}{8} - \frac{3 x^{\sqrt{\sin{\left(x \right)}}} \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x}\right) \left(2 \log{\left(x \right)} \sqrt{\sin{\left(x \right)}} + \frac{\log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{x \sqrt{\sin{\left(x \right)}}} + \frac{4 \sqrt{\sin{\left(x \right)}}}{x^{2}}\right)}{8} + \frac{\left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x}\right)^{3}}{8} - \frac{3 \left(\frac{\log{\left(x \right)} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x}\right) \left(2 \log{\left(x \right)} \sqrt{\sin{\left(x \right)}} + \frac{\log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{x \sqrt{\sin{\left(x \right)}}} + \frac{4 \sqrt{\sin{\left(x \right)}}}{x^{2}}\right)}{8} + \frac{\log{\left(x \right)} \cos{\left(x \right)}}{4 \sqrt{\sin{\left(x \right)}}} + \frac{3 \log{\left(x \right)} \cos^{3}{\left(x \right)}}{8 \sin^{\frac{5}{2}}{\left(x \right)}} - \frac{3 \sqrt{\sin{\left(x \right)}}}{2 x} - \frac{3 \cos^{2}{\left(x \right)}}{4 x \sin^{\frac{3}{2}}{\left(x \right)}} - \frac{3 \cos{\left(x \right)}}{2 x^{2} \sqrt{\sin{\left(x \right)}}} + \frac{2 \sqrt{\sin{\left(x \right)}}}{x^{3}}\right) e^{x^{\sqrt{\sin{\left(x \right)}}}}$$
Gráfico