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 2*cos(3*x)
-
Derivada de x^(2/5)
-
Derivada de 1/ln(x)
-
Derivada de x^((-2)/7)
-
Expresiones idénticas
- (x(e^x)arctgx)/(lnx)^ cinco
- (x(e en el grado x)arctgx) dividir por (lnx) en el grado 5
- (x(e en el grado x)arctgx) dividir por (lnx) en el grado cinco
- (x(ex)arctgx)/(lnx)5
- xexarctgx/lnx5
- (x(e^x)arctgx)/(lnx)⁵
- xe^xarctgx/lnx^5
- (x(e^x)arctgx) dividir por (lnx)^5
Derivada de (x(e^x)arctgx)/(lnx)^5
Solución
Ha introducido
[src]
x
x*E *acot(x)
------------
5
log (x)
$$\frac{e^{x} x \operatorname{acot}{\left(x \right)}}{\log{\left(x \right)}^{5}}$$
((x*E^x)*acot(x))/log(x)^5
Primera derivada
[src]
x
/ x x\ x*e
\E + x*e /*acot(x) - ------
2 x
1 + x 5*acot(x)*e
---------------------------- - ------------
5 6
log (x) log (x)
$$\frac{- \frac{x e^{x}}{x^{2} + 1} + \left(e^{x} + x e^{x}\right) \operatorname{acot}{\left(x \right)}}{\log{\left(x \right)}^{5}} - \frac{5 e^{x} \operatorname{acot}{\left(x \right)}}{\log{\left(x \right)}^{6}}$$
Segunda derivada
[src]
/ / x \ \
| 10*|------ - (1 + x)*acot(x)| / 6 \ |
| 2 | 2 | 5*|1 + ------|*acot(x)|
| 2*(1 + x) 2*x \1 + x / \ log(x)/ | x
|(2 + x)*acot(x) - --------- + --------- + ----------------------------- + ----------------------|*e
| 2 2 x*log(x) x*log(x) |
| 1 + x / 2\ |
\ \1 + x / /
-----------------------------------------------------------------------------------------------------
5
log (x)
$$\frac{\left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{acot}{\left(x \right)} + \frac{5 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \operatorname{acot}{\left(x \right)}}{x \log{\left(x \right)}} + \frac{10 \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}$$
Tercera derivada
[src]
/ / 2 \ \
| | 2*(1 + x) 2*x | / 2 \ |
| 15*|(2 + x)*acot(x) - --------- + ---------| | 4*x | / 6 \ / x \ / 9 21 \ |
| | 2 2| 2*x*|-1 + ------| 15*|1 + ------|*|------ - (1 + x)*acot(x)| 10*|1 + ------ + -------|*acot(x)|
| | 1 + x / 2\ | | 2| \ log(x)/ | 2 | | log(x) 2 | |
| 3*(2 + x) \ \1 + x / / \ 1 + x / 6*x*(1 + x) \1 + x / \ log (x)/ | x
|(3 + x)*acot(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)
$$\frac{\left(\frac{6 x \left(x + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(x + 2\right)}{x^{2} + 1} + \left(x + 3\right) \operatorname{acot}{\left(x \right)} - \frac{15 \left(\frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + 1\right)}{x^{2} + 1} + \left(x + 2\right) \operatorname{acot}{\left(x \right)}\right)}{x \log{\left(x \right)}} - \frac{15 \left(1 + \frac{6}{\log{\left(x \right)}}\right) \left(\frac{x}{x^{2} + 1} - \left(x + 1\right) \operatorname{acot}{\left(x \right)}\right)}{x^{2} \log{\left(x \right)}} - \frac{10 \left(1 + \frac{9}{\log{\left(x \right)}} + \frac{21}{\log{\left(x \right)}^{2}}\right) \operatorname{acot}{\left(x \right)}}{x^{2} \log{\left(x \right)}}\right) e^{x}}{\log{\left(x \right)}^{5}}$$
Gráfico