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 x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de (-2)/x^3
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Expresiones idénticas
- (x*sin(x))^log(x)*sin(x)
- (x multiplicar por seno de (x)) en el grado logaritmo de (x) multiplicar por seno de (x)
- (x*sin(x))log(x)*sin(x)
- x*sinxlogx*sinx
- (xsin(x))^log(x)sin(x)
- (xsin(x))log(x)sin(x)
- xsinxlogxsinx
- xsinx^logxsinx
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Expresiones semejantes
- (x*sinx)^log(x)*sinx
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Expresiones con funciones
- Seno sin
- sin(x)-x
- sin(x)/(x*cos(x))
- sin(x)/log(x)
- sin(x+(pi/4))
- sin(x)/(x^2+1)
- Logaritmo log
- log^2(x)
- log2(5x+3)
- log(x+cos(x))^(2)
- log(x*sin(x)+cos(x))
- log((x+1)/(x-1))
- Seno sin
- sin(x)-x
- sin(x)/(x*cos(x))
- sin(x)/log(x)
- sin(x+(pi/4))
- sin(x)/(x^2+1)
Derivada de (x*sin(x))^log(x)*sin(x)
Solución
Ha introducido
[src]
log(x) (x*sin(x)) *sin(x)
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)}} \sin{\left(x \right)}$$
(x*sin(x))^log(x)*sin(x)
Solución detallada
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
; calculamos :
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La derivada del seno es igual al coseno:
Como resultado de:
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Respuesta:
Primera derivada
[src]
log(x) log(x) /log(x*sin(x)) (x*cos(x) + sin(x))*log(x)\
(x*sin(x)) *cos(x) + (x*sin(x)) *|------------- + --------------------------|*sin(x)
\ x x*sin(x) /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)}} \left(\frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{\log{\left(x \sin{\left(x \right)} \right)}}{x}\right) \sin{\left(x \right)} + \left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)}} \cos{\left(x \right)}$$
Segunda derivada
[src]
/ / 2 \ \
| | /(x*cos(x) + sin(x))*log(x) \ | |
| | |-------------------------- + log(x*sin(x))| | |
| |log(x*sin(x)) \ sin(x) / (-2*cos(x) + x*sin(x))*log(x) 2*(x*cos(x) + sin(x)) (x*cos(x) + sin(x))*log(x) (x*cos(x) + sin(x))*cos(x)*log(x)| |
| |------------- - --------------------------------------------- + ----------------------------- - --------------------- + -------------------------- + ---------------------------------|*sin(x) /(x*cos(x) + sin(x))*log(x) \ |
| | x x sin(x) x*sin(x) x*sin(x) 2 | 2*|-------------------------- + log(x*sin(x))|*cos(x)|
log(x) | \ sin (x) / \ sin(x) / |
(x*sin(x)) *|-sin(x) - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------|
\ x x /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)}} \left(- \sin{\left(x \right)} + \frac{2 \left(\frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right) \cos{\left(x \right)}}{x} - \frac{\left(\frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} - \frac{\left(\frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right)^{2}}{x} + \frac{\log{\left(x \sin{\left(x \right)} \right)}}{x}\right) \sin{\left(x \right)}}{x}\right)$$
Tercera derivada
[src]
/ / 3 /(x*cos(x) + sin(x))*log(x) \ /log(x*sin(x)) (-2*cos(x) + x*sin(x))*log(x) 2*(x*cos(x) + sin(x)) (x*cos(x) + sin(x))*log(x) (x*cos(x) + sin(x))*cos(x)*log(x)\ \ / 2 \ \
| |/(x*cos(x) + sin(x))*log(x) \ 3*|-------------------------- + log(x*sin(x))|*|------------- + ----------------------------- - --------------------- + -------------------------- + ---------------------------------| | | /(x*cos(x) + sin(x))*log(x) \ | |
| ||-------------------------- + log(x*sin(x))| \ sin(x) / | x sin(x) x*sin(x) x*sin(x) 2 | 2 | | |-------------------------- + log(x*sin(x))| | |
| |\ sin(x) / 2*log(x*sin(x)) (x*cos(x) + sin(x))*log(x) (3*sin(x) + x*cos(x))*log(x) 6*(x*cos(x) + sin(x)) 3*(-2*cos(x) + x*sin(x)) \ sin (x) / 3*(x*cos(x) + sin(x))*cos(x) 2*(-2*cos(x) + x*sin(x))*log(x) 2*(x*cos(x) + sin(x))*log(x) 2*cos (x)*(x*cos(x) + sin(x))*log(x) 2*(-2*cos(x) + x*sin(x))*cos(x)*log(x) 2*(x*cos(x) + sin(x))*cos(x)*log(x)| |log(x*sin(x)) \ sin(x) / (-2*cos(x) + x*sin(x))*log(x) 2*(x*cos(x) + sin(x)) (x*cos(x) + sin(x))*log(x) (x*cos(x) + sin(x))*cos(x)*log(x)| |
| |--------------------------------------------- + --------------- + -------------------------- - ---------------------------- - --------------------- - ------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------- + ------------------------------- + ---------------------------- + ------------------------------------ + -------------------------------------- + -----------------------------------|*sin(x) /(x*cos(x) + sin(x))*log(x) \ 3*|------------- - --------------------------------------------- + ----------------------------- - --------------------- + -------------------------- + ---------------------------------|*cos(x)|
| | 2 2 sin(x) sin(x) 2 x*sin(x) x 2 x*sin(x) 2 3 2 2 | 3*|-------------------------- + log(x*sin(x))|*sin(x) | x x sin(x) x*sin(x) x*sin(x) 2 | |
log(x) | \ x x x *sin(x) x*sin (x) x *sin(x) sin (x) sin (x) x*sin (x) / \ sin(x) / \ sin (x) / |
(x*sin(x)) *|-cos(x) + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\ x x x /
$$\left(x \sin{\left(x \right)}\right)^{\log{\left(x \right)}} \left(- \cos{\left(x \right)} - \frac{3 \left(\frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right) \sin{\left(x \right)}}{x} - \frac{3 \left(\frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} - \frac{\left(\frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right)^{2}}{x} + \frac{\log{\left(x \sin{\left(x \right)} \right)}}{x}\right) \cos{\left(x \right)}}{x} + \frac{\left(\frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos^{2}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{3 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \cos{\left(x \right)}}{x \sin^{2}{\left(x \right)}} - \frac{3 \left(\frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right) \left(\frac{\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x \sin{\left(x \right)}} + \frac{\log{\left(x \sin{\left(x \right)} \right)}}{x}\right)}{x} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{6 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{2} \sin{\left(x \right)}} + \frac{\left(\frac{\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)}}{\sin{\left(x \right)}} + \log{\left(x \sin{\left(x \right)} \right)}\right)^{3}}{x^{2}} + \frac{2 \log{\left(x \sin{\left(x \right)} \right)}}{x^{2}}\right) \sin{\left(x \right)}}{x}\right)$$
Gráfico