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
-
¿Cómo usar?
- Derivada de:
-
Derivada de (π-2x)³
-
Derivada de y=e×
-
Derivada de y/(sqrt(5^2+y^2))
-
Derivada de y=(3x-7)4
-
Expresiones idénticas
- (x*e^x*arctg(x))/(ln(x))^ cinco
- (x multiplicar por e en el grado x multiplicar por arctg(x)) dividir por (ln(x)) en el grado 5
- (x multiplicar por e en el grado x multiplicar por arctg(x)) dividir por (ln(x)) en el grado cinco
- (x*ex*arctg(x))/(ln(x))5
- x*ex*arctgx/lnx5
- (x*e^x*arctg(x))/(ln(x))⁵
- (xe^xarctg(x))/(ln(x))^5
- (xexarctg(x))/(ln(x))5
- xexarctgx/lnx5
- xe^xarctgx/lnx^5
- (x*e^x*arctg(x)) dividir por (ln(x))^5
Derivada de (x*e^x*arctg(x))/(ln(x))^5
Solución
Ha introducido
[src]
x
x*E *atan(x)
------------
5
log (x)
$$\frac{e^{x} x \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}}$$
((x*E^x)*atan(x))/log(x)^5
Primera derivada
[src]
x
/ x x\ x*e
\E + x*e /*atan(x) + ------
2 x
1 + x 5*atan(x)*e
---------------------------- - ------------
5 6
log (x) log (x)
$$\frac{\frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{5}} - \frac{5 e^{x} \operatorname{atan}{\left(x \right)}}{\log{\left(x \right)}^{6}}$$
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)/ | x
|(2 + x)*atan(x) - --------- + --------- - ----------------------------- + ----------------------|*e
| 2 2 x*log(x) x*log(x) |
| / 2\ 1 + x |
\ \1 + x / /
-----------------------------------------------------------------------------------------------------
5
log (x)
$$\frac{\left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)} + \frac{5 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{x \log{\left(x \right)}} - \frac{10 \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right)}{x \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}$$
Tercera derivada
[src]
/ / 2 \ \
| | 2*x 2*(1 + x)| / 2 \ |
| 15*|(2 + x)*atan(x) - --------- + ---------| | 4*x | / 9 21 \ / 6 \ / x \|
| | 2 2 | 2*x*|-1 + ------| 10*|1 + ------ + -------|*atan(x) 15*|1 + ------|*|------ + (1 + x)*atan(x)||
| | / 2\ 1 + x | | 2| | log(x) 2 | \ log(x)/ | 2 ||
| 3*(2 + x) \ \1 + x / / 6*x*(1 + x) \ 1 + x / \ log (x)/ \1 + x /| x
|(3 + x)*atan(x) + --------- - -------------------------------------------- - ----------- + ----------------- - --------------------------------- + ------------------------------------------|*e
| 2 x*log(x) 2 2 2 2 |
| 1 + x / 2\ / 2\ x *log(x) x *log(x) |
\ \1 + x / \1 + x / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
5
log (x)
$$\frac{\left(- \frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(x + 2\right)}{x^{2} + 1} + \left(x + 3\right) \operatorname{atan}{\left(x \right)} - \frac{15 \left(- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{atan}{\left(x \right)}\right)}{x \log{\left(x \right)}} + \frac{15 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \left(\frac{x}{x^{2} + 1} + \left(x + 1\right) \operatorname{atan}{\left(x \right)}\right)}{x^{2} \log{\left(x \right)}} - \frac{10 \left(1 + \frac{9}{\log{\left(x \right)}} + \frac{21}{\log{\left(x \right)}^{2}}\right) \operatorname{atan}{\left(x \right)}}{x^{2} \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}$$
Gráfico