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:
- Derivada de e^((3*x)^2)
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Derivada de d/dx(x)
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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Expresiones idénticas
- y=(cos5x)^lnx
- y es igual a ( coseno de 5x) en el grado lnx
- y=(cos5x)lnx
- y=cos5xlnx
- y=cos5x^lnx
Derivada de y=(cos5x)^lnx
Solución
Ha introducido
[src]
log(x) cos (5*x)
$$\cos^{\log{\left(x \right)}}{\left(5 x \right)}$$
cos(5*x)^log(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
log(x) /log(cos(5*x)) 5*log(x)*sin(5*x)\
cos (5*x)*|------------- - -----------------|
\ x cos(5*x) /
$$\left(- \frac{5 \log{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} + \frac{\log{\left(\cos{\left(5 x \right)} \right)}}{x}\right) \cos^{\log{\left(x \right)}}{\left(5 x \right)}$$
Segunda derivada
[src]
/ 2 2 \
log(x) |/ log(cos(5*x)) 5*log(x)*sin(5*x)\ log(cos(5*x)) 25*sin (5*x)*log(x) 10*sin(5*x)|
cos (5*x)*||- ------------- + -----------------| - 25*log(x) - ------------- - ------------------- - -----------|
|\ x cos(5*x) / 2 2 x*cos(5*x)|
\ x cos (5*x) /
$$\left(\left(\frac{5 \log{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{\log{\left(\cos{\left(5 x \right)} \right)}}{x}\right)^{2} - \frac{25 \log{\left(x \right)} \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} - 25 \log{\left(x \right)} - \frac{10 \sin{\left(5 x \right)}}{x \cos{\left(5 x \right)}} - \frac{\log{\left(\cos{\left(5 x \right)} \right)}}{x^{2}}\right) \cos^{\log{\left(x \right)}}{\left(5 x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 3 2 \
log(x) | / log(cos(5*x)) 5*log(x)*sin(5*x)\ 75 2*log(cos(5*x)) / log(cos(5*x)) 5*log(x)*sin(5*x)\ | log(cos(5*x)) 10*sin(5*x) 25*sin (5*x)*log(x)| 250*log(x)*sin(5*x) 250*sin (5*x)*log(x) 75*sin (5*x) 15*sin(5*x)|
cos (5*x)*|- |- ------------- + -----------------| - -- + --------------- + 3*|- ------------- + -----------------|*|25*log(x) + ------------- + ----------- + -------------------| - ------------------- - -------------------- - ------------ + -----------|
| \ x cos(5*x) / x 3 \ x cos(5*x) / | 2 x*cos(5*x) 2 | cos(5*x) 3 2 2 |
\ x \ x cos (5*x) / cos (5*x) x*cos (5*x) x *cos(5*x)/
$$\left(- \left(\frac{5 \log{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{\log{\left(\cos{\left(5 x \right)} \right)}}{x}\right)^{3} + 3 \left(\frac{5 \log{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{\log{\left(\cos{\left(5 x \right)} \right)}}{x}\right) \left(\frac{25 \log{\left(x \right)} \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 25 \log{\left(x \right)} + \frac{10 \sin{\left(5 x \right)}}{x \cos{\left(5 x \right)}} + \frac{\log{\left(\cos{\left(5 x \right)} \right)}}{x^{2}}\right) - \frac{250 \log{\left(x \right)} \sin^{3}{\left(5 x \right)}}{\cos^{3}{\left(5 x \right)}} - \frac{250 \log{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{75 \sin^{2}{\left(5 x \right)}}{x \cos^{2}{\left(5 x \right)}} - \frac{75}{x} + \frac{15 \sin{\left(5 x \right)}}{x^{2} \cos{\left(5 x \right)}} + \frac{2 \log{\left(\cos{\left(5 x \right)} \right)}}{x^{3}}\right) \cos^{\log{\left(x \right)}}{\left(5 x \right)}$$
Gráfico