Sr Examen

Otras calculadoras

((xexp^3x)*arcctgx^2)/(2-(ln)^5(x))
Derivada de la función/ ((xexp^3x)*arcctgx^2)/(2-(ln)^5(x))

Derivada de ((xexp^3x)*arcctgx^2)/(2-(ln)^5(x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   3       2   
x*E *x*acot (x)
---------------
        5      
 2 - log (x)*x
xe3xacot⁡2(x)−xlog⁡(x)5+2\frac{x e^{3} x \operatorname{acot}^{2}{\left(x \right)}}{- x \log{\left(x \right)}^{5} + 2} 
(((x*E^3)*x)*acot(x)^2)/(2 - log(x)^5*x)
Gráfica
02468-8-6-4-2-10102000-1000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                            2          3                                       
    2    /   3      3\   2*x *acot(x)*e                                        
acot (x)*\x*E  + x*e / - ---------------                                       
                                   2        2     2    /   5           4   \  3
                              1 + x        x *acot (x)*\log (x) + 5*log (x)/*e 
---------------------------------------- + ------------------------------------
                    5                                               2          
             2 - log (x)*x                           /       5     \           
                                                     \2 - log (x)*x/
x2(log⁡(x)5+5log⁡(x)4)e3acot⁡2(x)(−xlog⁡(x)5+2)2+−2x2e3acot⁡(x)x2+1+(e3x+xe3)acot⁡2(x)−xlog⁡(x)5+2\frac{x^{2} \left(\log{\left(x \right)}^{5} + 5 \log{\left(x \right)}^{4}\right) e^{3} \operatorname{acot}^{2}{\left(x \right)}}{\left(- x \log{\left(x \right)}^{5} + 2\right)^{2}} + \frac{- \frac{2 x^{2} e^{3} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \left(e^{3} x + x e^{3}\right) \operatorname{acot}^{2}{\left(x \right)}}{- x \log{\left(x \right)}^{5} + 2}
Simplificar
Segunda derivada [src] 
 /                                                                        /                                 2    5   \                                                       \    
 |                                                     2     2       3    |  5*(4 + log(x))   2*(5 + log(x)) *log (x)|          4                 /             x   \        |    
 |                                                    x *acot (x)*log (x)*|- -------------- + -----------------------|   4*x*log (x)*(5 + log(x))*|-acot(x) + ------|*acot(x)|    
 |                              2                                         |        x                         5       |                            |                2|        |    
 |      2      8*x*acot(x)   2*x *(1 + 2*x*acot(x))                       \                        -2 + x*log (x)    /                            \           1 + x /        |  3 
-|2*acot (x) - ----------- + ---------------------- + ---------------------------------------------------------------- + ----------------------------------------------------|*e  
 |                     2                   2                                             5                                                            5                      |    
 |                1 + x            /     2\                                    -2 + x*log (x)                                               -2 + x*log (x)                   |    
 \                                 \1 + x /                                                                                                                                  /    
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                            5                                                                                     
                                                                                  -2 + x*log (x)
−(x2(2(log⁡(x)+5)2log⁡(x)5xlog⁡(x)5−2−5(log⁡(x)+4)x)log⁡(x)3acot⁡2(x)xlog⁡(x)5−2+2x2(2xacot⁡(x)+1)(x2+1)2+4x(xx2+1−acot⁡(x))(log⁡(x)+5)log⁡(x)4acot⁡(x)xlog⁡(x)5−2−8xacot⁡(x)x2+1+2acot⁡2(x))e3xlog⁡(x)5−2- \frac{\left(\frac{x^{2} \left(\frac{2 \left(\log{\left(x \right)} + 5\right)^{2} \log{\left(x \right)}^{5}}{x \log{\left(x \right)}^{5} - 2} - \frac{5 \left(\log{\left(x \right)} + 4\right)}{x}\right) \log{\left(x \right)}^{3} \operatorname{acot}^{2}{\left(x \right)}}{x \log{\left(x \right)}^{5} - 2} + \frac{2 x^{2} \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{4 x \left(\frac{x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right) \left(\log{\left(x \right)} + 5\right) \log{\left(x \right)}^{4} \operatorname{acot}{\left(x \right)}}{x \log{\left(x \right)}^{5} - 2} - \frac{8 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + 2 \operatorname{acot}^{2}{\left(x \right)}\right) e^{3}}{x \log{\left(x \right)}^{5} - 2}
Simplificar
Tercera derivada [src] 
/  /               /                       2        \                        \                                                                                                                                                                                                                                                                            \   
|  |             2 |            3*x     4*x *acot(x)|                        |                                                                                                                                                                                                                                                                            |   
|  |            x *|-acot(x) + ------ + ------------|                        |                          /            2                                \                       /  /         2   \                 3    10            5                             \                                                                                       |   
|  |               |                2           2   |                        |        4                 |    2      x *(1 + 2*x*acot(x))   4*x*acot(x)|    2     2       2    |5*\-12 + log (x)/   6*(5 + log(x)) *log  (x)   30*log (x)*(4 + log(x))*(5 + log(x))|                                   /                                 2    5   \        |   
|  |               \           1 + x       1 + x    /   3*x*(1 + 2*x*acot(x))|   6*log (x)*(5 + log(x))*|acot (x) + -------------------- - -----------|   x *acot (x)*log (x)*|----------------- - ------------------------ + ------------------------------------|          3    /             x   \ |  5*(4 + log(x))   2*(5 + log(x)) *log (x)|        |   
|4*|3*acot(x) + ------------------------------------- - ---------------------|                          |                        2                 2  |                       |         2                             2                  /          5   \         |   6*x*log (x)*|-acot(x) + ------|*|- -------------- + -----------------------|*acot(x)|   
|  |                                 2                               2       |                          |                /     2\             1 + x   |                       |        x              /          5   \                 x*\-2 + x*log (x)/         |               |                2| |        x                         5       |        |   
|  \                            1 + x                           1 + x        /                          \                \1 + x /                     /                       \                       \-2 + x*log (x)/                                            /               \           1 + x / \                        -2 + x*log (x)    /        |  3
|----------------------------------------------------------------------------- + ---------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------|*e 
|                                         2                                                                            5                                                                                          5                                                                                                5                                      |   
\                                    1 + x                                                                   -2 + x*log (x)                                                                             -2 + x*log (x)                                                                                   -2 + x*log (x)                                   /   
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                  5                                                                                                                                                                           
                                                                                                                                                                        -2 + x*log (x)
(−x2(−6(log⁡(x)+5)3log⁡(x)10(xlog⁡(x)5−2)2+30(log⁡(x)+4)(log⁡(x)+5)log⁡(x)5x(xlog⁡(x)5−2)+5(log⁡(x)2−12)x2)log⁡(x)2acot⁡2(x)xlog⁡(x)5−2+6x(xx2+1−acot⁡(x))(2(log⁡(x)+5)2log⁡(x)5xlog⁡(x)5−2−5(log⁡(x)+4)x)log⁡(x)3acot⁡(x)xlog⁡(x)5−2+6(log⁡(x)+5)(x2(2xacot⁡(x)+1)(x2+1)2−4xacot⁡(x)x2+1+acot⁡2(x))log⁡(x)4xlog⁡(x)5−2+4(x2(4x2acot⁡(x)x2+1+3xx2+1−acot⁡(x))x2+1−3x(2xacot⁡(x)+1)x2+1+3acot⁡(x))x2+1)e3xlog⁡(x)5−2\frac{\left(- \frac{x^{2} \left(- \frac{6 \left(\log{\left(x \right)} + 5\right)^{3} \log{\left(x \right)}^{10}}{\left(x \log{\left(x \right)}^{5} - 2\right)^{2}} + \frac{30 \left(\log{\left(x \right)} + 4\right) \left(\log{\left(x \right)} + 5\right) \log{\left(x \right)}^{5}}{x \left(x \log{\left(x \right)}^{5} - 2\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 12\right)}{x^{2}}\right) \log{\left(x \right)}^{2} \operatorname{acot}^{2}{\left(x \right)}}{x \log{\left(x \right)}^{5} - 2} + \frac{6 x \left(\frac{x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right) \left(\frac{2 \left(\log{\left(x \right)} + 5\right)^{2} \log{\left(x \right)}^{5}}{x \log{\left(x \right)}^{5} - 2} - \frac{5 \left(\log{\left(x \right)} + 4\right)}{x}\right) \log{\left(x \right)}^{3} \operatorname{acot}{\left(x \right)}}{x \log{\left(x \right)}^{5} - 2} + \frac{6 \left(\log{\left(x \right)} + 5\right) \left(\frac{x^{2} \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \operatorname{acot}^{2}{\left(x \right)}\right) \log{\left(x \right)}^{4}}{x \log{\left(x \right)}^{5} - 2} + \frac{4 \left(\frac{x^{2} \left(\frac{4 x^{2} \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} - \operatorname{acot}{\left(x \right)}\right)}{x^{2} + 1} - \frac{3 x \left(2 x \operatorname{acot}{\left(x \right)} + 1\right)}{x^{2} + 1} + 3 \operatorname{acot}{\left(x \right)}\right)}{x^{2} + 1}\right) e^{3}}{x \log{\left(x \right)}^{5} - 2}
Simplificar
Gráfico
Derivada de ((xexp^3x)*arcctgx^2)/(2-(ln)^5(x))
    © Sr Examen – Калькулятор