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^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- x^sinc×sinx
- x en el grado seno de c× seno de x
- xsinc×sinx
Derivada de x^sinc×sinx
Solución
Ha introducido
[src]
sinc(x) x *sin(x)
$$x^{\operatorname{sinc}{\left(x \right)}} \sin{\left(x \right)}$$
x^sinc(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]
/ //-sin(x) + x*cos(x) \ \
| ||------------------ for x != 0| |
sinc(x) sinc(x) |sinc(x) || 2 | |
x *cos(x) + x *|------- + |< x |*log(x)|*sin(x)
| x || | |
| || 0 otherwise | |
\ \\ / /
$$x^{\operatorname{sinc}{\left(x \right)}} \left(\left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{\operatorname{sinc}{\left(x \right)}}{x}\right) \sin{\left(x \right)} + x^{\operatorname{sinc}{\left(x \right)}} \cos{\left(x \right)}$$
Segunda derivada
[src]
/ / //-sin(x) + x*cos(x) \\ \
| | ||------------------ for x != 0|| |
| | || 2 || |
| | 2 // /2*(-sin(x) + x*cos(x)) \ \ 2*|< x || |
| |/ //-sin(x) + x*cos(x) \ \ ||-|---------------------- + sin(x)| | || || / //-sin(x) + x*cos(x) \ \ |
| || ||------------------ for x != 0| | || | 2 | | || 0 otherwise || | ||------------------ for x != 0| | |
sinc(x) | ||sinc(x) || 2 | | || \ x / | sinc(x) \\ /| |sinc(x) || 2 | | |
x *|-sin(x) + ||------- + |< x |*log(x)| + |<----------------------------------- for x != 0|*log(x) - ------- + -----------------------------------|*sin(x) + 2*|------- + |< x |*log(x)|*cos(x)|
| || x || | | || x | 2 x | | x || | | |
| || || 0 otherwise | | || | x | | || 0 otherwise | | |
| |\ \\ / / || 0 otherwise | | \ \\ / / |
\ \ \\ / / /
$$x^{\operatorname{sinc}{\left(x \right)}} \left(2 \left(\left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{\operatorname{sinc}{\left(x \right)}}{x}\right) \cos{\left(x \right)} + \left(\left(\left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{\operatorname{sinc}{\left(x \right)}}{x}\right)^{2} + \left(\begin{cases} - \frac{\sin{\left(x \right)} + \frac{2 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{2}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{2 \left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{x} - \frac{\operatorname{sinc}{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)} - \sin{\left(x \right)}\right)$$
Tercera derivada
[src]
/ / // /2*(-sin(x) + x*cos(x)) \ \ \ \
| | ||-|---------------------- + sin(x)| | | |
| | //-sin(x) + x*cos(x) \ || | 2 | | / //-sin(x) + x*cos(x) \\| / //-sin(x) + x*cos(x) \\ |
| | ||------------------ for x != 0| || \ x / | | ||------------------ for x != 0||| | ||------------------ for x != 0|| |
| | || 2 | 3*|<----------------------------------- for x != 0| | || 2 ||| | || 2 || |
| | 3 // 3*sin(x) 6*(-sin(x) + x*cos(x)) \ 3*|< x | || x | |// /2*(-sin(x) + x*cos(x)) \ \ 2*|< x ||| | 2 // /2*(-sin(x) + x*cos(x)) \ \ 2*|< x || |
| |/ //-sin(x) + x*cos(x) \ \ ||-cos(x) + -------- + ---------------------- | || | || | / //-sin(x) + x*cos(x) \ \ |||-|---------------------- + sin(x)| | || ||| / //-sin(x) + x*cos(x) \ \ |/ //-sin(x) + x*cos(x) \ \ ||-|---------------------- + sin(x)| | || || |
| || ||------------------ for x != 0| | || x 3 | || 0 otherwise | || 0 otherwise | | ||------------------ for x != 0| | ||| | 2 | | || 0 otherwise ||| | ||------------------ for x != 0| | || ||------------------ for x != 0| | || | 2 | | || 0 otherwise || |
sinc(x) | ||sinc(x) || 2 | | || x | \\ / 2*sinc(x) \\ / |sinc(x) || 2 | | ||| \ x / | sinc(x) \\ /|| |sinc(x) || 2 | | ||sinc(x) || 2 | | || \ x / | sinc(x) \\ /| |
x *|-cos(x) + ||------- + |< x |*log(x)| + |<------------------------------------------- for x != 0|*log(x) - ----------------------------------- + --------- + ---------------------------------------------------- + 3*|------- + |< x |*log(x)|*||<----------------------------------- for x != 0|*log(x) - ------- + -----------------------------------||*sin(x) - 3*|------- + |< x |*log(x)|*sin(x) + 3*||------- + |< x |*log(x)| + |<----------------------------------- for x != 0|*log(x) - ------- + -----------------------------------|*cos(x)|
| || x || | | || x | 2 3 x | x || | | ||| x | 2 x || | x || | | || x || | | || x | 2 x | |
| || || 0 otherwise | | || | x x | || 0 otherwise | | ||| | x || | || 0 otherwise | | || || 0 otherwise | | || | x | |
| |\ \\ / / || 0 otherwise | \ \\ / / ||| 0 otherwise | || \ \\ / / |\ \\ / / || 0 otherwise | | |
\ \ \\ / \\\ / // \ \\ / / /
$$x^{\operatorname{sinc}{\left(x \right)}} \left(- 3 \left(\left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{\operatorname{sinc}{\left(x \right)}}{x}\right) \sin{\left(x \right)} + 3 \left(\left(\left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{\operatorname{sinc}{\left(x \right)}}{x}\right)^{2} + \left(\begin{cases} - \frac{\sin{\left(x \right)} + \frac{2 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{2}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{2 \left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{x} - \frac{\operatorname{sinc}{\left(x \right)}}{x^{2}}\right) \cos{\left(x \right)} + \left(\left(\left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{\operatorname{sinc}{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{\operatorname{sinc}{\left(x \right)}}{x}\right) \left(\left(\begin{cases} - \frac{\sin{\left(x \right)} + \frac{2 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{2}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{2 \left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{x} - \frac{\operatorname{sinc}{\left(x \right)}}{x^{2}}\right) + \left(\begin{cases} \frac{- \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{6 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{3}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right) \log{\left(x \right)} + \frac{3 \left(\begin{cases} - \frac{\sin{\left(x \right)} + \frac{2 \left(x \cos{\left(x \right)} - \sin{\left(x \right)}\right)}{x^{2}}}{x} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{x} - \frac{3 \left(\begin{cases} \frac{x \cos{\left(x \right)} - \sin{\left(x \right)}}{x^{2}} & \text{for}\: x \neq 0 \\0 & \text{otherwise} \end{cases}\right)}{x^{2}} + \frac{2 \operatorname{sinc}{\left(x \right)}}{x^{3}}\right) \sin{\left(x \right)} - \cos{\left(x \right)}\right)$$
Gráfico