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 -2*y
-
Derivada de 3^2*x
-
Derivada de 2*x+8/x
-
Derivada de -1/y
-
Expresiones idénticas
- (x×sin(x))^(ln((x^ dos)+ uno))
- (x× seno de (x)) en el grado (ln((x al cuadrado ) más 1))
- (x× seno de (x)) en el grado (ln((x en el grado dos) más uno))
- (x×sin(x))(ln((x2)+1))
- x×sinxlnx2+1
- (x×sin(x))^(ln((x²)+1))
- (x×sin(x)) en el grado (ln((x en el grado 2)+1))
- x×sinx^lnx^2+1
-
Expresiones semejantes
- (x×sin(x))^(ln((x^2)-1))
- (x×sinx)^(ln((x^2)+1))
-
Expresiones con funciones
- Seno sin
- sin(x)^4
- sin(x/3+3)+2*x
- sin^5*x
- sin^4(x^2-7)
- sin(x^2-7)^(4)
- ln
- ln(x+10)^11
- ln((x^2)-1)
- ln3x^5
- ln^3(x^2+1)
- ln(1+|x|)
Derivada de (x×sin(x))^(ln((x^2)+1))
Solución
Ha introducido
[src]
/ 2 \
log\x + 1/
(x*sin(x))
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x^{2} + 1 \right)}}$$
(x*sin(x))^log(x^2 + 1)
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
-
Simplificamos:
Respuesta:
Primera derivada
[src]
/ 2 \ / / 2 \\
log\x + 1/ |2*x*log(x*sin(x)) (x*cos(x) + sin(x))*log\x + 1/|
(x*sin(x)) *|----------------- + -------------------------------|
| 2 x*sin(x) |
\ x + 1 /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x^{2} + 1 \right)}} \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}}\right)$$
Segunda derivada
[src]
/ 2 \
/ 2\ |/ / 2\\ 2 / 2\ / 2\ / 2\|
log\1 + x / ||2*x*log(x*sin(x)) (x*cos(x) + sin(x))*log\1 + x /| 2*log(x*sin(x)) 4*x *log(x*sin(x)) 4*(x*cos(x) + sin(x)) (-2*cos(x) + x*sin(x))*log\1 + x / (x*cos(x) + sin(x))*log\1 + x / (x*cos(x) + sin(x))*cos(x)*log\1 + x /|
(x*sin(x)) *||----------------- + -------------------------------| + --------------- - ------------------ + --------------------- - ---------------------------------- - ------------------------------- - --------------------------------------|
|| 2 x*sin(x) | 2 2 / 2\ x*sin(x) 2 2 |
|\ 1 + x / 1 + x / 2\ \1 + x /*sin(x) x *sin(x) x*sin (x) |
\ \1 + x / /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x^{2} + 1 \right)}} \left(- \frac{4 x^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}}\right)^{2} + \frac{4 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right) \sin{\left(x \right)}} + \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} - \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x^{2} \sin{\left(x \right)}}\right)$$
Tercera derivada
[src]
/ 3 \
/ 2\ |/ / 2\\ / / 2\\ / 2 / 2\ / 2\ / 2\\ 3 / 2\ / 2\ / 2\ / 2\ 2 / 2\ / 2\ / 2\|
log\1 + x / ||2*x*log(x*sin(x)) (x*cos(x) + sin(x))*log\1 + x /| |2*x*log(x*sin(x)) (x*cos(x) + sin(x))*log\1 + x /| | 2*log(x*sin(x)) 4*(x*cos(x) + sin(x)) 4*x *log(x*sin(x)) (-2*cos(x) + x*sin(x))*log\1 + x / (x*cos(x) + sin(x))*log\1 + x / (x*cos(x) + sin(x))*cos(x)*log\1 + x /| 12*x*log(x*sin(x)) 6*(-2*cos(x) + x*sin(x)) 16*x *log(x*sin(x)) (x*cos(x) + sin(x))*log\1 + x / (3*sin(x) + x*cos(x))*log\1 + x / 12*x*(x*cos(x) + sin(x)) 6*(x*cos(x) + sin(x))*cos(x) 2*(x*cos(x) + sin(x))*log\1 + x / 2*(-2*cos(x) + x*sin(x))*log\1 + x / 2*cos (x)*(x*cos(x) + sin(x))*log\1 + x / 2*(-2*cos(x) + x*sin(x))*cos(x)*log\1 + x / 2*(x*cos(x) + sin(x))*cos(x)*log\1 + x /|
(x*sin(x)) *||----------------- + -------------------------------| - 3*|----------------- + -------------------------------|*|- --------------- - --------------------- + ------------------ + ---------------------------------- + ------------------------------- + --------------------------------------| - ------------------ - ------------------------ + ------------------- + ------------------------------- - --------------------------------- - ------------------------ - ---------------------------- + --------------------------------- + ------------------------------------ + ----------------------------------------- + ------------------------------------------- + ----------------------------------------|
|| 2 x*sin(x) | | 2 x*sin(x) | | 2 / 2\ 2 x*sin(x) 2 2 | 2 / 2\ 3 x*sin(x) x*sin(x) 2 / 2\ 2 3 2 3 2 2 2 |
|\ 1 + x / \ 1 + x / | 1 + x \1 + x /*sin(x) / 2\ x *sin(x) x*sin (x) | / 2\ \1 + x /*sin(x) / 2\ / 2\ \1 + x /*sin (x) x *sin(x) x *sin(x) x*sin (x) x*sin (x) x *sin (x) |
\ \ \1 + x / / \1 + x / \1 + x / \1 + x / *sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x^{2} + 1 \right)}} \left(\frac{16 x^{3} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2} \sin{\left(x \right)}} - \frac{12 x \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}}\right)^{3} - 3 \left(\frac{2 x \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}}\right) \left(\frac{4 x^{2} \log{\left(x \sin{\left(x \right)} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{4 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right) \sin{\left(x \right)}} - \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2} + 1} + \frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x^{2} \sin{\left(x \right)}}\right) - \frac{6 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{\left(x^{2} + 1\right) \sin{\left(x \right)}} - \frac{6 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{\left(x^{2} + 1\right) \sin^{2}{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)} \cos^{2}{\left(x \right)}}{x \sin^{3}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x \sin{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x^{2} \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)} \cos{\left(x \right)}}{x^{2} \sin^{2}{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x^{2} + 1 \right)}}{x^{3} \sin{\left(x \right)}}\right)$$
Gráfico