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
-
¿Cómo usar?
- Derivada de:
-
Derivada de 1/(x+1)^2
-
Derivada de (x+3)/(x-1)
-
Derivada de (1-2*x)^3
-
Derivada de x^3/x
-
Expresiones idénticas
- y=(ln(x))^cos3x
- y es igual a (ln(x)) en el grado coseno de 3x
- y=(ln(x))cos3x
- y=lnxcos3x
- y=lnx^cos3x
-
Expresiones con funciones
- ln
- ln(1+2x)
- ln((1+x)/(1-x))
- ln(x-3)
- ln(x^1/2)
- ln(tg(x))
Derivada de y=(ln(x))^cos3x
Solución
Ha introducido
[src]
cos(3*x) log (x)
$$\log{\left(x \right)}^{\cos{\left(3 x \right)}}$$
log(x)^cos(3*x)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
cos(3*x) / cos(3*x)\
log (x)*|-3*log(log(x))*sin(3*x) + --------|
\ x*log(x)/
$$\left(- 3 \log{\left(\log{\left(x \right)} \right)} \sin{\left(3 x \right)} + \frac{\cos{\left(3 x \right)}}{x \log{\left(x \right)}}\right) \log{\left(x \right)}^{\cos{\left(3 x \right)}}$$
Segunda derivada
[src]
/ 2 \
cos(3*x) |/ cos(3*x)\ cos(3*x) cos(3*x) 6*sin(3*x)|
log (x)*||3*log(log(x))*sin(3*x) - --------| - 9*cos(3*x)*log(log(x)) - --------- - ---------- - ----------|
|\ x*log(x)/ 2 2 2 x*log(x) |
\ x *log(x) x *log (x) /
$$\left(\left(3 \log{\left(\log{\left(x \right)} \right)} \sin{\left(3 x \right)} - \frac{\cos{\left(3 x \right)}}{x \log{\left(x \right)}}\right)^{2} - 9 \log{\left(\log{\left(x \right)} \right)} \cos{\left(3 x \right)} - \frac{6 \sin{\left(3 x \right)}}{x \log{\left(x \right)}} - \frac{\cos{\left(3 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\cos{\left(3 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\cos{\left(3 x \right)}}$$
Tercera derivada
[src]
/ 3 \
cos(3*x) | / cos(3*x)\ / cos(3*x)\ / cos(3*x) cos(3*x) 6*sin(3*x)\ 27*cos(3*x) 2*cos(3*x) 2*cos(3*x) 3*cos(3*x) 9*sin(3*x) 9*sin(3*x)|
log (x)*|- |3*log(log(x))*sin(3*x) - --------| + 3*|3*log(log(x))*sin(3*x) - --------|*|9*cos(3*x)*log(log(x)) + --------- + ---------- + ----------| + 27*log(log(x))*sin(3*x) - ----------- + ---------- + ---------- + ---------- + ---------- + ----------|
| \ x*log(x)/ \ x*log(x)/ | 2 2 2 x*log(x) | x*log(x) 3 3 3 3 2 2 2 2 |
\ \ x *log(x) x *log (x) / x *log(x) x *log (x) x *log (x) x *log(x) x *log (x)/
$$\left(- \left(3 \log{\left(\log{\left(x \right)} \right)} \sin{\left(3 x \right)} - \frac{\cos{\left(3 x \right)}}{x \log{\left(x \right)}}\right)^{3} + 3 \left(3 \log{\left(\log{\left(x \right)} \right)} \sin{\left(3 x \right)} - \frac{\cos{\left(3 x \right)}}{x \log{\left(x \right)}}\right) \left(9 \log{\left(\log{\left(x \right)} \right)} \cos{\left(3 x \right)} + \frac{6 \sin{\left(3 x \right)}}{x \log{\left(x \right)}} + \frac{\cos{\left(3 x \right)}}{x^{2} \log{\left(x \right)}} + \frac{\cos{\left(3 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) + 27 \log{\left(\log{\left(x \right)} \right)} \sin{\left(3 x \right)} - \frac{27 \cos{\left(3 x \right)}}{x \log{\left(x \right)}} + \frac{9 \sin{\left(3 x \right)}}{x^{2} \log{\left(x \right)}} + \frac{9 \sin{\left(3 x \right)}}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \cos{\left(3 x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \cos{\left(3 x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \cos{\left(3 x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\cos{\left(3 x \right)}}$$
Gráfico