Sr Examen

Derivada de (x+e^x)arctgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
/     x\        
\x + E /*acot(x)
$$\left(e^{x} + x\right) \operatorname{acot}{\left(x \right)}$$
(x + E^x)*acot(x)
Gráfica
Primera derivada [src]
                        x
/     x\           x + E 
\1 + E /*acot(x) - ------
                        2
                   1 + x 
$$\left(e^{x} + 1\right) \operatorname{acot}{\left(x \right)} - \frac{e^{x} + x}{x^{2} + 1}$$
Segunda derivada [src]
               /     x\       /     x\
         x   2*\1 + e /   2*x*\x + e /
acot(x)*e  - ---------- + ------------
                    2              2  
               1 + x       /     2\   
                           \1 + x /   
$$\frac{2 x \left(x + e^{x}\right)}{\left(x^{2} + 1\right)^{2}} + e^{x} \operatorname{acot}{\left(x \right)} - \frac{2 \left(e^{x} + 1\right)}{x^{2} + 1}$$
Tercera derivada [src]
                        /         2 \                        
                        |      4*x  | /     x\               
                      2*|-1 + ------|*\x + e /               
                 x      |          2|                /     x\
         x    3*e       \     1 + x /            6*x*\1 + e /
acot(x)*e  - ------ - ------------------------ + ------------
                  2                  2                    2  
             1 + x           /     2\             /     2\   
                             \1 + x /             \1 + x /   
$$\frac{6 x \left(e^{x} + 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 \left(x + e^{x}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + e^{x} \operatorname{acot}{\left(x \right)} - \frac{3 e^{x}}{x^{2} + 1}$$
Gráfico
Derivada de (x+e^x)arctgx