Sr Examen

Otras calculadoras

y=x^e^arctgx
Derivada de la función/ y=x^e/ arctg/ y=x^e^arctgx

Derivada de y=x^e^arctgx

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 / acot(x)\
 \E       /
x
xeacot⁡(x)x^{e^{\operatorname{acot}{\left(x \right)}}} 
x^(E^acot(x))
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(eacot⁡(x))+1)eeacot⁡(x)acot⁡(x)\left(\log{\left(e^{\operatorname{acot}{\left(x \right)}} \right)} + 1\right) e^{e^{\operatorname{acot}{\left(x \right)}} \operatorname{acot}{\left(x \right)}}

  2. Simplificamos:

    (acot⁡(x)+1)eeacot⁡(x)acot⁡(x)\left(\operatorname{acot}{\left(x \right)} + 1\right) e^{e^{\operatorname{acot}{\left(x \right)}} \operatorname{acot}{\left(x \right)}}

Respuesta:

(acot⁡(x)+1)eeacot⁡(x)acot⁡(x)\left(\operatorname{acot}{\left(x \right)} + 1\right) e^{e^{\operatorname{acot}{\left(x \right)}} \operatorname{acot}{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 / acot(x)\ / acot(x)    acot(x)       \
 \E       / |e          e       *log(x)|
x          *|-------- - ---------------|
            |   x                 2    |
            \                1 + x     /
xeacot⁡(x)(−eacot⁡(x)log⁡(x)x2+1+eacot⁡(x)x)x^{e^{\operatorname{acot}{\left(x \right)}}} \left(- \frac{e^{\operatorname{acot}{\left(x \right)}} \log{\left(x \right)}}{x^{2} + 1} + \frac{e^{\operatorname{acot}{\left(x \right)}}}{x}\right)
Simplificar
Segunda derivada [src] 
 / acot(x)\ /                                 2                                   \         
 \e       / |  1      log(x)    /  1   log(x)\   acot(x)       2        2*x*log(x)|  acot(x)
x          *|- -- + --------- + |- - + ------| *e        - ---------- + ----------|*e       
            |   2           2   |  x        2|               /     2\           2 |         
            |  x    /     2\    \      1 + x /             x*\1 + x /   /     2\  |         
            \       \1 + x /                                            \1 + x /  /
xeacot⁡(x)(2xlog⁡(x)(x2+1)2+(log⁡(x)x2+1−1x)2eacot⁡(x)+log⁡(x)(x2+1)2−2x(x2+1)−1x2)eacot⁡(x)x^{e^{\operatorname{acot}{\left(x \right)}}} \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{\log{\left(x \right)}}{x^{2} + 1} - \frac{1}{x}\right)^{2} e^{\operatorname{acot}{\left(x \right)}} + \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x \left(x^{2} + 1\right)} - \frac{1}{x^{2}}\right) e^{\operatorname{acot}{\left(x \right)}}
Simplificar
Tercera derivada [src] 
 / acot(x)\ /                                           3                                                         2                                                                                             \         
 \e       / |2        6         log(x)    /  1   log(x)\   2*acot(x)    2*log(x)        3             3        8*x *log(x)   6*x*log(x)     /  1   log(x)\ /  1      log(x)        2        2*x*log(x)\  acot(x)|  acot(x)
x          *|-- + --------- - --------- - |- - + ------| *e          + --------- + ----------- + ----------- - ----------- - ---------- - 3*|- - + ------|*|- -- + --------- - ---------- + ----------|*e       |*e       
            | 3           2           3   |  x        2|                       2             2    2 /     2\            3            3      |  x        2| |   2           2     /     2\           2 |         |         
            |x    /     2\    /     2\    \      1 + x /               /     2\      /     2\    x *\1 + x /    /     2\     /     2\       \      1 + x / |  x    /     2\    x*\1 + x /   /     2\  |         |         
            \     \1 + x /    \1 + x /                                 \1 + x /    x*\1 + x /                   \1 + x /     \1 + x /                      \       \1 + x /                 \1 + x /  /         /
xeacot⁡(x)(−8x2log⁡(x)(x2+1)3−6xlog⁡(x)(x2+1)3−(log⁡(x)x2+1−1x)3e2acot⁡(x)−3(log⁡(x)x2+1−1x)(2xlog⁡(x)(x2+1)2+log⁡(x)(x2+1)2−2x(x2+1)−1x2)eacot⁡(x)+2log⁡(x)(x2+1)2+6(x2+1)2−log⁡(x)(x2+1)3+3x(x2+1)2+3x2(x2+1)+2x3)eacot⁡(x)x^{e^{\operatorname{acot}{\left(x \right)}}} \left(- \frac{8 x^{2} \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \left(\frac{\log{\left(x \right)}}{x^{2} + 1} - \frac{1}{x}\right)^{3} e^{2 \operatorname{acot}{\left(x \right)}} - 3 \left(\frac{\log{\left(x \right)}}{x^{2} + 1} - \frac{1}{x}\right) \left(\frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x \left(x^{2} + 1\right)} - \frac{1}{x^{2}}\right) e^{\operatorname{acot}{\left(x \right)}} + \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{\left(x^{2} + 1\right)^{2}} - \frac{\log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{3}{x \left(x^{2} + 1\right)^{2}} + \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2}{x^{3}}\right) e^{\operatorname{acot}{\left(x \right)}}
Simplificar
Gráfico
Derivada de y=x^e^arctgx
    © Sr Examen – Калькулятор