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