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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 1/(x+3)
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Derivada de 4*y
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Derivada de (-1)/x-3*x
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Derivada de y=csc(3x²+1)
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Expresiones idénticas
- x*e^x*atan(x)/log(x)^(cinco *x)
- x multiplicar por e en el grado x multiplicar por arco tangente de gente de (x) dividir por logaritmo de (x) en el grado (5 multiplicar por x)
- x multiplicar por e en el grado x multiplicar por arco tangente de gente de (x) dividir por logaritmo de (x) en el grado (cinco multiplicar por x)
- x*ex*atan(x)/log(x)(5*x)
- x*ex*atanx/logx5*x
- xe^xatan(x)/log(x)^(5x)
- xexatan(x)/log(x)(5x)
- xexatanx/logx5x
- xe^xatanx/logx^5x
- x*e^x*atan(x) dividir por log(x)^(5*x)
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Expresiones semejantes
- x*e^x*arctan(x)/log(x)^(5*x)
- x*e^x*arctanx/log(x)^(5*x)
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Expresiones con funciones
- Logaritmo log
- log(1)
- log(acos(1/sqrt(x)))
- log(x+1)+1
- log(6+6/x)
- log(4+3*x)
Derivada de x*e^x*atan(x)/log(x)^(5*x)
Solución
Ha introducido
[src]
x
x*E *atan(x)
------------
5*x
log (x)
$$\frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5 x}}$$
((x*E^x)*atan(x))/log(x)^(5*x)
Primera derivada
[src]
/ x \
-5*x |/ x x\ x*e | -5*x / 5 \ x
log (x)*|\E + x*e /*atan(x) + ------| + x*log (x)*|- ------ - 5*log(log(x))|*atan(x)*e
| 2| \ log(x) /
\ 1 + x /
$$x \left(- 5 \log{\left(\log{\left(x \right)} \right)} - \frac{5}{\log{\left(x \right)}}\right) e^{x} \log{\left(x \right)}^{- 5 x} \operatorname{atan}{\left(x \right)} + \left(\frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{atan}{\left(x \right)}\right) \log{\left(x \right)}^{- 5 x}$$
Segunda derivada
[src]
/ / 1 \ \
| 2 | 2 1 - ------| |
-5*x | / 1 \ / x \ 2*x 2*(1 + x) | / 1 \ log(x)| | x
log (x)*|(2 + x)*atan(x) - 10*|------ + log(log(x))|*|------ + (1 + x)*atan(x)| - --------- + --------- + 5*x*|5*|------ + log(log(x))| - ----------|*atan(x)|*e
| \log(x) / | 2 | 2 2 \ \log(x) / x*log(x) / |
| \1 + x / / 2\ 1 + x |
\ \1 + x / /
$$\left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + 5 x \left(5 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} - \frac{1 - \frac{1}{\log{\left(x \right)}}}{x \log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)} - 10 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)\right) e^{x} \log{\left(x \right)}^{- 5 x}$$
Tercera derivada
[src]
/ / 2 \ \
| | 4*x | / 2 \ |
| / 1 \ 2*x*|-1 + ------| | 1 - ------- / 1 \ / 1 \| |
| / 2 \ | 2 1 - ------| | 2| | 3 2 15*|1 - ------|*|------ + log(log(x))|| |
-5*x | / 1 \ | 2*x 2*(1 + x)| 3*(2 + x) | / 1 \ log(x)| / x \ 6*x*(1 + x) \ 1 + x / | / 1 \ log (x) \ log(x)/ \log(x) /| | x
log (x)*|(3 + x)*atan(x) - 15*|------ + log(log(x))|*|(2 + x)*atan(x) - --------- + ---------| + --------- + 15*|5*|------ + log(log(x))| - ----------|*|------ + (1 + x)*atan(x)| - ----------- + ----------------- + 5*x*|- 25*|------ + log(log(x))| + ----------- + --------------------------------------|*atan(x)|*e
| \log(x) / | 2 2 | 2 \ \log(x) / x*log(x) / | 2 | 2 2 | \log(x) / 2 x*log(x) | |
| | / 2\ 1 + x | 1 + x \1 + x / / 2\ / 2\ \ x *log(x) / |
\ \ \1 + x / / \1 + x / \1 + x / /
$$\left(- \frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} + 5 x \left(- 25 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{3} + \frac{15 \left(1 - \frac{1}{\log{\left(x \right)}}\right) \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)}{x \log{\left(x \right)}} + \frac{1 - \frac{2}{\log{\left(x \right)}^{2}}}{x^{2} \log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(x + 2\right)}{x^{2} + 1} + \left(x + 3\right) \operatorname{atan}{\left(x \right)} + 15 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right) \left(5 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right)^{2} - \frac{1 - \frac{1}{\log{\left(x \right)}}}{x \log{\left(x \right)}}\right) - 15 \left(\log{\left(\log{\left(x \right)} \right)} + \frac{1}{\log{\left(x \right)}}\right) \left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)}\right)\right) e^{x} \log{\left(x \right)}^{- 5 x}$$
Gráfico