Sr Examen

Derivada de y=e^arctg3x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 atan(3*x)
E         
$$e^{\operatorname{atan}{\left(3 x \right)}}$$
E^atan(3*x)
Gráfica
Primera derivada [src]
   atan(3*x)
3*e         
------------
         2  
  1 + 9*x   
$$\frac{3 e^{\operatorname{atan}{\left(3 x \right)}}}{9 x^{2} + 1}$$
Segunda derivada [src]
             atan(3*x)
9*(1 - 6*x)*e         
----------------------
               2      
     /       2\       
     \1 + 9*x /       
$$\frac{9 \left(1 - 6 x\right) e^{\operatorname{atan}{\left(3 x \right)}}}{\left(9 x^{2} + 1\right)^{2}}$$
3-я производная [src]
   /                                2  \           
   |        1         18*x      72*x   |  atan(3*x)
27*|-2 + -------- - -------- + --------|*e         
   |            2          2          2|           
   \     1 + 9*x    1 + 9*x    1 + 9*x /           
---------------------------------------------------
                              2                    
                    /       2\                     
                    \1 + 9*x /                     
$$\frac{27 \left(\frac{72 x^{2}}{9 x^{2} + 1} - \frac{18 x}{9 x^{2} + 1} - 2 + \frac{1}{9 x^{2} + 1}\right) e^{\operatorname{atan}{\left(3 x \right)}}}{\left(9 x^{2} + 1\right)^{2}}$$
Tercera derivada [src]
   /                                2  \           
   |        1         18*x      72*x   |  atan(3*x)
27*|-2 + -------- - -------- + --------|*e         
   |            2          2          2|           
   \     1 + 9*x    1 + 9*x    1 + 9*x /           
---------------------------------------------------
                              2                    
                    /       2\                     
                    \1 + 9*x /                     
$$\frac{27 \left(\frac{72 x^{2}}{9 x^{2} + 1} - \frac{18 x}{9 x^{2} + 1} - 2 + \frac{1}{9 x^{2} + 1}\right) e^{\operatorname{atan}{\left(3 x \right)}}}{\left(9 x^{2} + 1\right)^{2}}$$
Gráfico
Derivada de y=e^arctg3x