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 e^((3*x)^2)
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Derivada de d/dx(x)
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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Expresiones idénticas
- ((x^k))*(exp^(-x))/k!
- ((x en el grado k)) multiplicar por ( exponente de en el grado ( menos x)) dividir por k!
- ((xk))*(exp(-x))/k!
- xk*exp-x/k!
- ((x^k))(exp^(-x))/k!
- ((xk))(exp(-x))/k!
- xkexp-x/k!
- x^kexp^-x/k!
- ((x^k))*(exp^(-x)) dividir por k!
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Expresiones semejantes
- ((x^k))*(exp^(x))/k!
Derivada de ((x^k))*(exp^(-x))/k!
Solución
Primera derivada
[src]
k -x k -x
x *e *log(x) x *e *Gamma(1 + k)*polygamma(0, 1 + k)
------------- - ---------------------------------------
k! 2
k!
$$\frac{x^{k} e^{- x} \log{\left(x \right)}}{k!} - \frac{x^{k} e^{- x} \Gamma\left(k + 1\right) \operatorname{polygamma}{\left(0,k + 1 \right)}}{k!^{2}}$$
Segunda derivada
[src]
/ / 2 \ \
| | 2 2*polygamma (0, 1 + k)*Gamma(1 + k) | |
| |polygamma (0, 1 + k) - ----------------------------------- + polygamma(1, 1 + k)|*Gamma(1 + k) |
k | 2 \ k! / 2*Gamma(1 + k)*log(x)*polygamma(0, 1 + k)| -x
x *|log (x) - ----------------------------------------------------------------------------------------------- - -----------------------------------------|*e
\ k! k! /
--------------------------------------------------------------------------------------------------------------------------------------------------------------
k!
$$\frac{x^{k} \left(- \frac{\left(\operatorname{polygamma}^{2}{\left(0,k + 1 \right)} + \operatorname{polygamma}{\left(1,k + 1 \right)} - \frac{2 \Gamma\left(k + 1\right) \operatorname{polygamma}^{2}{\left(0,k + 1 \right)}}{k!}\right) \Gamma\left(k + 1\right)}{k!} + \log{\left(x \right)}^{2} - \frac{2 \log{\left(x \right)} \Gamma\left(k + 1\right) \operatorname{polygamma}{\left(0,k + 1 \right)}}{k!}\right) e^{- x}}{k!}$$
Tercera derivada
[src]
/ / 3 2 3 \ \
| | 3 6*polygamma (0, 1 + k)*Gamma(1 + k) 6*Gamma (1 + k)*polygamma (0, 1 + k) 6*Gamma(1 + k)*polygamma(0, 1 + k)*polygamma(1, 1 + k) | / 2 \ |
| |polygamma (0, 1 + k) + 3*polygamma(0, 1 + k)*polygamma(1, 1 + k) - ----------------------------------- + ------------------------------------ - ------------------------------------------------------ + polygamma(2, 1 + k)|*Gamma(1 + k) | 2 2*polygamma (0, 1 + k)*Gamma(1 + k) | |
| | k! 2 k! | 2 3*|polygamma (0, 1 + k) - ----------------------------------- + polygamma(1, 1 + k)|*Gamma(1 + k)*log(x)|
k | 3 \ k! / 3*log (x)*Gamma(1 + k)*polygamma(0, 1 + k) \ k! / | -x
x *|log (x) - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------ - --------------------------------------------------------------------------------------------------------|*e
\ k! k! k! /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
k!
$$\frac{x^{k} \left(- \frac{3 \left(\operatorname{polygamma}^{2}{\left(0,k + 1 \right)} + \operatorname{polygamma}{\left(1,k + 1 \right)} - \frac{2 \Gamma\left(k + 1\right) \operatorname{polygamma}^{2}{\left(0,k + 1 \right)}}{k!}\right) \log{\left(x \right)} \Gamma\left(k + 1\right)}{k!} - \frac{\left(\operatorname{polygamma}^{3}{\left(0,k + 1 \right)} + 3 \operatorname{polygamma}{\left(0,k + 1 \right)} \operatorname{polygamma}{\left(1,k + 1 \right)} + \operatorname{polygamma}{\left(2,k + 1 \right)} - \frac{6 \Gamma\left(k + 1\right) \operatorname{polygamma}^{3}{\left(0,k + 1 \right)}}{k!} - \frac{6 \Gamma\left(k + 1\right) \operatorname{polygamma}{\left(0,k + 1 \right)} \operatorname{polygamma}{\left(1,k + 1 \right)}}{k!} + \frac{6 \Gamma^{2}\left(k + 1\right) \operatorname{polygamma}^{3}{\left(0,k + 1 \right)}}{k!^{2}}\right) \Gamma\left(k + 1\right)}{k!} + \log{\left(x \right)}^{3} - \frac{3 \log{\left(x \right)}^{2} \Gamma\left(k + 1\right) \operatorname{polygamma}{\left(0,k + 1 \right)}}{k!}\right) e^{- x}}{k!}$$