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 (-4)/x^2
-
Derivada de 2/x²
-
Derivada de -2*y
-
Derivada de (3+2x)/(x-5)
-
Expresiones idénticas
- (x+sin6x)^x^ dos
- (x más seno de 6x) en el grado x al cuadrado
- (x más seno de 6x) en el grado x en el grado dos
- (x+sin6x)x2
- x+sin6xx2
- (x+sin6x)^x²
- (x+sin6x) en el grado x en el grado 2
- x+sin6x^x^2
-
Expresiones semejantes
- (x-sin6x)^x^2
Derivada de (x+sin6x)^x^2
Solución
Ha introducido
[src]
/ 2\
\x /
(x + sin(6*x))
$$\left(x + \sin{\left(6 x \right)}\right)^{x^{2}}$$
(x + sin(6*x))^(x^2)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ 2\ / 2 \
\x / | x *(1 + 6*cos(6*x))|
(x + sin(6*x)) *|2*x*log(x + sin(6*x)) + -------------------|
\ x + sin(6*x) /
$$\left(x + \sin{\left(6 x \right)}\right)^{x^{2}} \left(\frac{x^{2} \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 x \log{\left(x + \sin{\left(6 x \right)} \right)}\right)$$
Segunda derivada
[src]
/ 2\ / 2 2 2 2 \
\x / | 2 / x*(1 + 6*cos(6*x))\ x *(1 + 6*cos(6*x)) 36*x *sin(6*x) 4*x*(1 + 6*cos(6*x))|
(x + sin(6*x)) *|2*log(x + sin(6*x)) + x *|2*log(x + sin(6*x)) + ------------------| - -------------------- - -------------- + --------------------|
| \ x + sin(6*x) / 2 x + sin(6*x) x + sin(6*x) |
\ (x + sin(6*x)) /
$$\left(x + \sin{\left(6 x \right)}\right)^{x^{2}} \left(x^{2} \left(\frac{x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right)^{2} - \frac{36 x^{2} \sin{\left(6 x \right)}}{x + \sin{\left(6 x \right)}} - \frac{x^{2} \left(6 \cos{\left(6 x \right)} + 1\right)^{2}}{\left(x + \sin{\left(6 x \right)}\right)^{2}} + \frac{4 x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right)$$
Tercera derivada
[src]
/ / 2 3 2 2 \ \
| | 2 x *(1 + 6*cos(6*x)) 3*x*(1 + 6*cos(6*x)) 54*x *(1 + 6*cos(6*x))*sin(6*x)| |
| 2*|-3 - 18*cos(6*x) + 108*x*sin(6*x) + 108*x *cos(6*x) - -------------------- + --------------------- - -------------------------------| |
/ 2\ | 3 | 2 x + sin(6*x) x + sin(6*x) | / 2 2 2 \|
\x / | 3 / x*(1 + 6*cos(6*x))\ \ (x + sin(6*x)) / / x*(1 + 6*cos(6*x))\ | x *(1 + 6*cos(6*x)) 4*x*(1 + 6*cos(6*x)) 36*x *sin(6*x)||
(x + sin(6*x)) *|x *|2*log(x + sin(6*x)) + ------------------| - ---------------------------------------------------------------------------------------------------------------------------------------- - 3*x*|2*log(x + sin(6*x)) + ------------------|*|-2*log(x + sin(6*x)) + -------------------- - -------------------- + --------------||
| \ x + sin(6*x) / x + sin(6*x) \ x + sin(6*x) / | 2 x + sin(6*x) x + sin(6*x) ||
\ \ (x + sin(6*x)) //
$$\left(x + \sin{\left(6 x \right)}\right)^{x^{2}} \left(x^{3} \left(\frac{x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right)^{3} - 3 x \left(\frac{x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right) \left(\frac{36 x^{2} \sin{\left(6 x \right)}}{x + \sin{\left(6 x \right)}} + \frac{x^{2} \left(6 \cos{\left(6 x \right)} + 1\right)^{2}}{\left(x + \sin{\left(6 x \right)}\right)^{2}} - \frac{4 x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} - 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right) - \frac{2 \left(108 x^{2} \cos{\left(6 x \right)} - \frac{54 x^{2} \left(6 \cos{\left(6 x \right)} + 1\right) \sin{\left(6 x \right)}}{x + \sin{\left(6 x \right)}} - \frac{x^{2} \left(6 \cos{\left(6 x \right)} + 1\right)^{3}}{\left(x + \sin{\left(6 x \right)}\right)^{2}} + 108 x \sin{\left(6 x \right)} + \frac{3 x \left(6 \cos{\left(6 x \right)} + 1\right)^{2}}{x + \sin{\left(6 x \right)}} - 18 \cos{\left(6 x \right)} - 3\right)}{x + \sin{\left(6 x \right)}}\right)$$
Gráfico