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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- Derivada de:
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Derivada de -5*tan(2*t)-4*cot(4*t)
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Derivada de (3x+6)^2
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Derivada de 3^(x*x)
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Derivada de 2*x-8/x
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Expresiones idénticas
- (x*e^x*arctg*x)/(ln^ cinco)*x
- (x multiplicar por e en el grado x multiplicar por arctg multiplicar por x) dividir por (ln en el grado 5) multiplicar por x
- (x multiplicar por e en el grado x multiplicar por arctg multiplicar por x) dividir por (ln en el grado cinco) multiplicar por x
- (x*ex*arctg*x)/(ln5)*x
- x*ex*arctg*x/ln5*x
- (x*e^x*arctg*x)/(ln⁵)*x
- (xe^xarctgx)/(ln^5)x
- (xexarctgx)/(ln5)x
- xexarctgx/ln5x
- xe^xarctgx/ln^5x
- (x*e^x*arctg*x) dividir por (ln^5)*x
Derivada de (x*e^x*arctg*x)/(ln^5)*x
Solución
Ha introducido
[src]
x
x*E *atan(x)
------------*x
5
log (x)
$$x \frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}}$$
(((x*E^x)*atan(x))/log(x)^5)*x
Primera derivada
[src]
/ x \ |/ x x\ x*e | |\E + x*e /*atan(x) + ------ | | 2 x| x | 1 + x 5*atan(x)*e | x*E *atan(x) x*|---------------------------- - ------------| + ------------ | 5 6 | 5 \ log (x) log (x) / log (x)
$$x \left(\frac{\frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}} - \frac{5 e^{x} \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{6}}\right) + \frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}}$$
Segunda derivada
[src]
/ / / x \ \ \
| | 10*|------ + (1 + x)*atan(x)| / 6 \ | |
| | 2 | 2 | 5*|1 + ------|*atan(x)| |
| | 2*x 2*(1 + x) \1 + x / \ log(x)/ | 10*atan(x) 2*x | x
|x*|(2 + x)*atan(x) - --------- + --------- - ----------------------------- + ----------------------| - ---------- + ------ + 2*(1 + x)*atan(x)|*e
| | 2 2 x*log(x) x*log(x) | log(x) 2 |
| | / 2\ 1 + x | 1 + x |
\ \ \1 + x / / /
---------------------------------------------------------------------------------------------------------------------------------------------------
5
log (x)
$$\frac{\left(x \left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)} + \frac{5 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{x \log{\left(x \right)}} - \frac{10 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right)}{x \log{\left(x \right)}}\right) + \frac{2 x}{x^{2} + 1} + 2 \left(x + 1\right) \operatorname{atan}{\left(x \right)} - \frac{10 \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}$$
Tercera derivada
[src]
/ / / 2 \ \ \
| | | 2*x 2*(1 + x)| / 2 \ | |
| | 15*|(2 + x)*atan(x) - --------- + ---------| | 4*x | / 9 21 \ / 6 \ / x \| / x \ |
| | | 2 2 | 2*x*|-1 + ------| 10*|1 + ------ + -------|*atan(x) 15*|1 + ------|*|------ + (1 + x)*atan(x)|| 30*|------ + (1 + x)*atan(x)| / 6 \ |
| | | / 2\ 1 + x | | 2| | log(x) 2 | \ log(x)/ | 2 || 2 | 2 | 15*|1 + ------|*atan(x)|
| | 3*(2 + x) \ \1 + x / / 6*x*(1 + x) \ 1 + x / \ log (x)/ \1 + x /| 6*x 6*(1 + x) \1 + x / \ log(x)/ | x
|x*|(3 + x)*atan(x) + --------- - -------------------------------------------- - ----------- + ----------------- - --------------------------------- + ------------------------------------------| - --------- + 3*(2 + x)*atan(x) + --------- - ----------------------------- + -----------------------|*e
| | 2 x*log(x) 2 2 2 2 | 2 2 x*log(x) x*log(x) |
| | 1 + x / 2\ / 2\ x *log(x) x *log(x) | / 2\ 1 + x |
\ \ \1 + x / \1 + x / / \1 + x / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5
log (x)
$$\frac{\left(- \frac{6 x^{2}}{\left(x^{2} + 1\right)^{2}} + x \left(- \frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(x + 2\right)}{x^{2} + 1} + \left(x + 3\right) \operatorname{atan}{\left(x \right)} - \frac{15 \left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)}\right)}{x \log{\left(x \right)}} + \frac{15 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right)}{x^{2} \log{\left(x \right)}} - \frac{10 \left(1 + \frac{9}{\log{\left(x \right)}} + \frac{21}{\log{\left(x \right)}^{2}}\right) \operatorname{atan}{\left(x \right)}}{x^{2} \log{\left(x \right)}}\right) + \frac{6 \left(x + 1\right)}{x^{2} + 1} + 3 \left(x + 2\right) \operatorname{atan}{\left(x \right)} + \frac{15 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{x \log{\left(x \right)}} - \frac{30 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right)}{x \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}$$
Gráfico