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=(cos2x)^e^sinx
- y es igual a ( coseno de 2x) en el grado e en el grado seno de x
- y=(cos2x)esinx
- y=cos2xesinx
- y=cos2x^e^sinx
Derivada de y=(cos2x)^e^sinx
Solución
Ha introducido
[src]
/ sin(x)\
\E /
(cos(2*x))
$$\cos^{e^{\sin{\left(x \right)}}}{\left(2 x \right)}$$
cos(2*x)^(E^sin(x))
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]
/ sin(x)\ / sin(x) \
\E / | sin(x) 2*e *sin(2*x)|
(cos(2*x)) *|cos(x)*e *log(cos(2*x)) - ------------------|
\ cos(2*x) /
$$\left(e^{\sin{\left(x \right)}} \log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 e^{\sin{\left(x \right)}} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right) \cos^{e^{\sin{\left(x \right)}}}{\left(2 x \right)}$$
Segunda derivada
[src]
/ sin(x)\ / 2 2 \
\e / | / 2*sin(2*x)\ sin(x) 2 4*sin (2*x) 4*cos(x)*sin(2*x)| sin(x)
(cos(2*x)) *|-4 + |cos(x)*log(cos(2*x)) - ----------| *e + cos (x)*log(cos(2*x)) - log(cos(2*x))*sin(x) - ----------- - -----------------|*e
| \ cos(2*x) / 2 cos(2*x) |
\ cos (2*x) /
$$\left(\left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right)^{2} e^{\sin{\left(x \right)}} - \log{\left(\cos{\left(2 x \right)} \right)} \sin{\left(x \right)} + \log{\left(\cos{\left(2 x \right)} \right)} \cos^{2}{\left(x \right)} - \frac{4 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} - \frac{4 \sin{\left(2 x \right)} \cos{\left(x \right)}}{\cos{\left(2 x \right)}} - 4\right) e^{\sin{\left(x \right)}} \cos^{e^{\sin{\left(x \right)}}}{\left(2 x \right)}$$
Tercera derivada
[src]
/ sin(x)\ / 3 3 2 2 / 2 \ \
\e / | / 2*sin(2*x)\ 2*sin(x) 3 16*sin(2*x) 16*sin (2*x) 12*sin (2*x)*cos(x) 6*cos (x)*sin(2*x) / 2*sin(2*x)\ | 2 4*sin (2*x) 4*cos(x)*sin(2*x)| sin(x) 6*sin(x)*sin(2*x)| sin(x)
(cos(2*x)) *|-12*cos(x) + |cos(x)*log(cos(2*x)) - ----------| *e + cos (x)*log(cos(2*x)) - cos(x)*log(cos(2*x)) - ----------- - ------------ - ------------------- - ------------------ - 3*|cos(x)*log(cos(2*x)) - ----------|*|4 + log(cos(2*x))*sin(x) - cos (x)*log(cos(2*x)) + ----------- + -----------------|*e - 3*cos(x)*log(cos(2*x))*sin(x) + -----------------|*e
| \ cos(2*x) / cos(2*x) 3 2 cos(2*x) \ cos(2*x) / | 2 cos(2*x) | cos(2*x) |
\ cos (2*x) cos (2*x) \ cos (2*x) / /
$$\left(\left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right)^{3} e^{2 \sin{\left(x \right)}} - 3 \left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right) \left(\log{\left(\cos{\left(2 x \right)} \right)} \sin{\left(x \right)} - \log{\left(\cos{\left(2 x \right)} \right)} \cos^{2}{\left(x \right)} + \frac{4 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{4 \sin{\left(2 x \right)} \cos{\left(x \right)}}{\cos{\left(2 x \right)}} + 4\right) e^{\sin{\left(x \right)}} - 3 \log{\left(\cos{\left(2 x \right)} \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \log{\left(\cos{\left(2 x \right)} \right)} \cos^{3}{\left(x \right)} - \log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} - \frac{16 \sin^{3}{\left(2 x \right)}}{\cos^{3}{\left(2 x \right)}} - \frac{12 \sin^{2}{\left(2 x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(2 x \right)}} - \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(x \right)}}{\cos{\left(2 x \right)}} - \frac{16 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} - 12 \cos{\left(x \right)}\right) e^{\sin{\left(x \right)}} \cos^{e^{\sin{\left(x \right)}}}{\left(2 x \right)}$$
Gráfico