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 d/dx(x)
- Derivada de c/x
-
Derivada de (cos(x))^x^2
- Derivada de a^(2*x)
- Gráfico de la función y =:
- (xsinx)^(2/x)
-
Expresiones idénticas
- (xsinx)^(dos /x)
- (x seno de x) en el grado (2 dividir por x)
- (x seno de x) en el grado (dos dividir por x)
- (xsinx)(2/x)
- xsinx2/x
- xsinx^2/x
- (xsinx)^(2 dividir por x)
Derivada de (xsinx)^(2/x)
Solución
Ha introducido
[src]
2
-
x
(x*sin(x))
$$\left(x \sin{\left(x \right)}\right)^{\frac{2}{x}}$$
(x*sin(x))^(2/x)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
2
-
x / 2*log(x*sin(x)) 2*(x*cos(x) + sin(x))\
(x*sin(x)) *|- --------------- + ---------------------|
| 2 2 |
\ x x *sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{\frac{2}{x}} \left(\frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{2} \sin{\left(x \right)}} - \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2}}\right)$$
Segunda derivada
[src]
/ 2 \
2 | / x*cos(x) + sin(x)\ |
- | 2*|-log(x*sin(x)) + -----------------| |
x | -2*cos(x) + x*sin(x) 2*log(x*sin(x)) \ sin(x) / (x*cos(x) + sin(x))*cos(x) 3*(x*cos(x) + sin(x))|
2*(x*sin(x)) *|- -------------------- + --------------- + --------------------------------------- - -------------------------- - ---------------------|
| sin(x) x 2 2 x*sin(x) |
\ x sin (x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------
2
x
$$\frac{2 \left(x \sin{\left(x \right)}\right)^{\frac{2}{x}} \left(- \frac{x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x} + \frac{2 \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} - \log{\left(x \sin{\left(x \right)} \right)}\right)^{2}}{x^{2}}\right)}{x^{2}}$$
Tercera derivada
[src]
/ 3 / x*cos(x) + sin(x)\ /-2*cos(x) + x*sin(x) 2*log(x*sin(x)) (x*cos(x) + sin(x))*cos(x) 3*(x*cos(x) + sin(x))\ \
2 | / x*cos(x) + sin(x)\ 6*|-log(x*sin(x)) + -----------------|*|-------------------- - --------------- + -------------------------- + ---------------------| |
- | 4*|-log(x*sin(x)) + -----------------| \ sin(x) / | sin(x) x 2 x*sin(x) | 2 |
x |x*cos(x) + sin(x) 3*sin(x) + x*cos(x) 6*log(x*sin(x)) \ sin(x) / \ sin (x) / 2*cos (x)*(x*cos(x) + sin(x)) 2*(-2*cos(x) + x*sin(x))*cos(x) 5*(-2*cos(x) + x*sin(x)) 11*(x*cos(x) + sin(x)) 5*(x*cos(x) + sin(x))*cos(x)|
2*(x*sin(x)) *|----------------- - ------------------- - --------------- + --------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------- + ------------------------------- + ------------------------ + ---------------------- + ----------------------------|
| sin(x) sin(x) 2 4 2 3 2 x*sin(x) 2 2 |
\ x x x sin (x) sin (x) x *sin(x) x*sin (x) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
x
$$\frac{2 \left(x \sin{\left(x \right)}\right)^{\frac{2}{x}} \left(\frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos^{2}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{x \cos{\left(x \right)} + 3 \sin{\left(x \right)}}{\sin{\left(x \right)}} + \frac{5 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{5 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{11 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{2} \sin{\left(x \right)}} - \frac{6 \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} - \log{\left(x \sin{\left(x \right)} \right)}\right) \left(\frac{x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} - \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x}\right)}{x^{2}} - \frac{6 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2}} + \frac{4 \left(\frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{\sin{\left(x \right)}} - \log{\left(x \sin{\left(x \right)} \right)}\right)^{3}}{x^{4}}\right)}{x^{2}}$$
Gráfico