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:
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Derivada de x^-(4/5)
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Expresiones idénticas
- x^(sin(x)- uno)*sin(x)+x^(sin(x))*ln(x)*cos(x)
- x en el grado ( seno de (x) menos 1) multiplicar por seno de (x) más x en el grado ( seno de (x)) multiplicar por ln(x) multiplicar por coseno de (x)
- x en el grado ( seno de (x) menos uno) multiplicar por seno de (x) más x en el grado ( seno de (x)) multiplicar por ln(x) multiplicar por coseno de (x)
- x(sin(x)-1)*sin(x)+x(sin(x))*ln(x)*cos(x)
- xsinx-1*sinx+xsinx*lnx*cosx
- x^(sin(x)-1)sin(x)+x^(sin(x))ln(x)cos(x)
- x(sin(x)-1)sin(x)+x(sin(x))ln(x)cos(x)
- xsinx-1sinx+xsinxlnxcosx
- x^sinx-1sinx+x^sinxlnxcosx
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Expresiones semejantes
- x^(sin(x)+1)*sin(x)+x^(sin(x))*ln(x)*cos(x)
- x^(sin(x)-1)*sin(x)-x^(sin(x))*ln(x)*cos(x)
- x^(sinx-1)*sinx+x^(sinx)*ln(x)*cosx
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Expresiones con funciones
- Seno sin
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
- sin(x)^(2)/2
- sin(x^3)^2
- sin(x)^-1
- Seno sin
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
- sin(x)^(2)/2
- sin(x^3)^2
- sin(x)^-1
- Seno sin
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
- sin(x)^(2)/2
- sin(x^3)^2
- sin(x)^-1
- ln
- ln(x/5)
- ln(e^(2*x)+1)
- ln(x^2+2)
- ln(1+x²)
- ln√x-2
- Coseno cos
- cos^-1x
- cos(3x)/arccos(x)
- cos^(7)(4x^(3)-((5)/(x))+4x)
- cos3^x
- cos(x-4)
Derivada de x^(sin(x)-1)*sin(x)+x^(sin(x))*ln(x)*cos(x)
Solución
Ha introducido
[src]
sin(x) - 1 sin(x) x *sin(x) + x *log(x)*cos(x)
$$x^{\sin{\left(x \right)} - 1} \sin{\left(x \right)} + x^{\sin{\left(x \right)}} \log{\left(x \right)} \cos{\left(x \right)}$$
x^(sin(x) - 1)*sin(x) + (x^sin(x)*log(x))*cos(x)
Solución detallada
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diferenciamos miembro por miembro:
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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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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
; calculamos :
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Derivado es .
Como resultado de:
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; calculamos :
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La derivada del coseno es igual a menos el seno:
Como resultado de:
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Como resultado de:
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Simplificamos:
Respuesta:
Primera derivada
[src]
/ sin(x) \
sin(x) - 1 |x sin(x) /sin(x) \ | sin(x) - 1 /sin(x) - 1 \ sin(x)
x *cos(x) + |------- + x *|------ + cos(x)*log(x)|*log(x)|*cos(x) + x *|---------- + cos(x)*log(x)|*sin(x) - x *log(x)*sin(x)
\ x \ x / / \ x /
$$x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)} - 1}{x}\right) \sin{\left(x \right)} + x^{\sin{\left(x \right)} - 1} \cos{\left(x \right)} - x^{\sin{\left(x \right)}} \log{\left(x \right)} \sin{\left(x \right)} + \left(x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{x^{\sin{\left(x \right)}}}{x}\right) \cos{\left(x \right)}$$
Segunda derivada
[src]
/ /sin(x) \\
2 | 2 2*|------ + cos(x)*log(x)|| sin(x)
-1 + sin(x) -1 + sin(x) /-1 + sin(x) \ sin(x) | 1 /sin(x) \ /sin(x) 2*cos(x)\ \ x /| x *sin(x) -1 + sin(x) /-1 + sin(x) 2*cos(x)\ sin(x) /1 /sin(x) \ \ sin(x) -1 + sin(x) /-1 + sin(x) \ sin(x) /sin(x) \
- x *sin(x) + x *|----------- + cos(x)*log(x)| *sin(x) + x *|- -- + |------ + cos(x)*log(x)| *log(x) - |------ + log(x)*sin(x) - --------|*log(x) + --------------------------|*cos(x) - -------------- - x *|----------- + log(x)*sin(x) - --------|*sin(x) - x *|- + |------ + cos(x)*log(x)|*log(x)|*sin(x) - x *cos(x)*log(x) + 2*x *|----------- + cos(x)*log(x)|*cos(x) - x *|------ + cos(x)*log(x)|*log(x)*sin(x)
\ x / | 2 \ x / | 2 x | x | x | 2 x | \x \ x / / \ x / \ x /
\ x \ x / / \ x /
$$x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)} - 1}{x}\right)^{2} \sin{\left(x \right)} + 2 x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)} - 1}{x}\right) \cos{\left(x \right)} - x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)} - 1}{x^{2}}\right) \sin{\left(x \right)} - x^{\sin{\left(x \right)} - 1} \sin{\left(x \right)} - x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \sin{\left(x \right)} - x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \sin{\left(x \right)} + x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} - \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x} - \frac{1}{x^{2}}\right) \cos{\left(x \right)} - x^{\sin{\left(x \right)}} \log{\left(x \right)} \cos{\left(x \right)} - \frac{x^{\sin{\left(x \right)}} \sin{\left(x \right)}}{x}$$
Tercera derivada
[src]
/ 2 /sin(x) 2*cos(x)\ \
| /sin(x) \ 3*|------ + log(x)*sin(x) - --------| /sin(x) \ | / /sin(x) \\ sin(x) /sin(x) \
sin(x) 3 | 3 3*|------ + cos(x)*log(x)| | 2 x | 3*|------ + cos(x)*log(x)| | sin(x) | 2 2*|------ + cos(x)*log(x)|| 2 2 2*x *|------ + cos(x)*log(x)|*sin(x)
-1 + sin(x) x *sin(x) -1 + sin(x) /-1 + sin(x) \ sin(x) -1 + sin(x) / 2*(-1 + sin(x)) 3*sin(x) 3*cos(x)\ sin(x) /1 /sin(x) \ \ sin(x) | 2 / 2*sin(x) 3*sin(x) 3*cos(x)\ /sin(x) \ \ x / \ x / \ x / /sin(x) \ /sin(x) 2*cos(x)\ | -1 + sin(x) /-1 + sin(x) \ -1 + sin(x) /-1 + sin(x) 2*cos(x)\ 2*x *cos(x) sin(x) | 1 /sin(x) \ /sin(x) 2*cos(x)\ \ x /| -1 + sin(x) /-1 + sin(x) \ sin(x) /sin(x) 2*cos(x)\ sin(x) /sin(x) \ -1 + sin(x) /-1 + sin(x) \ /-1 + sin(x) 2*cos(x)\ \ x / sin(x) /sin(x) \
- x *cos(x) + -------------- + x *|----------- + cos(x)*log(x)| *sin(x) + x *log(x)*sin(x) - x *|cos(x)*log(x) - --------------- + -------- + --------|*sin(x) - x *|- + |------ + cos(x)*log(x)|*log(x)|*cos(x) - x *|- -- + |cos(x)*log(x) - -------- + -------- + --------|*log(x) - |------ + cos(x)*log(x)| *log(x) - --------------------------- + ------------------------------------- + -------------------------- + 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------|*log(x)|*cos(x) - 3*x *|----------- + cos(x)*log(x)|*sin(x) - 3*x *|----------- + log(x)*sin(x) - --------|*cos(x) - ---------------- - 2*x *|- -- + |------ + cos(x)*log(x)| *log(x) - |------ + log(x)*sin(x) - --------|*log(x) + --------------------------|*sin(x) + 3*x *|----------- + cos(x)*log(x)| *cos(x) + x *|------ + log(x)*sin(x) - --------|*log(x)*sin(x) - x *|------ + cos(x)*log(x)| *log(x)*sin(x) - 3*x *|----------- + cos(x)*log(x)|*|----------- + log(x)*sin(x) - --------|*sin(x) - ----------------------------------------- - 2*x *|------ + cos(x)*log(x)|*cos(x)*log(x)
2 \ x / | 3 x 2 | \x \ x / / | 3 | 3 x 2 | \ x / x x 2 \ x / | 2 x | | \ x / | 2 x | x | 2 \ x / | 2 x | x | \ x / | 2 x | \ x / \ x / | 2 x | x \ x /
x \ x x / \ x \ x x / x \ x / / \ x / \ x \ x / / \ x / \ x /
$$x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)} - 1}{x}\right)^{3} \sin{\left(x \right)} + 3 x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)} - 1}{x}\right)^{2} \cos{\left(x \right)} - 3 x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)} - 1}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)} - 1}{x^{2}}\right) \sin{\left(x \right)} - 3 x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)} - 1}{x}\right) \sin{\left(x \right)} - 3 x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)} - 1}{x^{2}}\right) \cos{\left(x \right)} - x^{\sin{\left(x \right)} - 1} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos{\left(x \right)}}{x^{2}} - \frac{2 \left(\sin{\left(x \right)} - 1\right)}{x^{3}}\right) \sin{\left(x \right)} - x^{\sin{\left(x \right)} - 1} \cos{\left(x \right)} - x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} + \frac{1}{x}\right) \cos{\left(x \right)} - x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \sin{\left(x \right)} - 2 x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \log{\left(x \right)} \cos{\left(x \right)} + x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \sin{\left(x \right)} - 2 x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} - \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} + \frac{2 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x} - \frac{1}{x^{2}}\right) \sin{\left(x \right)} - x^{\sin{\left(x \right)}} \left(- \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} \log{\left(x \right)} + 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} + \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)} - \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2}}{x} + \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right)}{x} + \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)}{x^{2}} - \frac{2}{x^{3}}\right) \cos{\left(x \right)} + x^{\sin{\left(x \right)}} \log{\left(x \right)} \sin{\left(x \right)} - \frac{2 x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{x} - \frac{2 x^{\sin{\left(x \right)}} \cos{\left(x \right)}}{x} + \frac{x^{\sin{\left(x \right)}} \sin{\left(x \right)}}{x^{2}}$$
Gráfico