Sr Examen

Derivada de y=arctgxln2x

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

Gráfico:

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Solución

Ha introducido [src]
acot(x)*log(2*x)
$$\log{\left(2 x \right)} \operatorname{acot}{\left(x \right)}$$
acot(x)*log(2*x)
Gráfica
Primera derivada [src]
acot(x)   log(2*x)
------- - --------
   x            2 
           1 + x  
$$- \frac{\log{\left(2 x \right)}}{x^{2} + 1} + \frac{\operatorname{acot}{\left(x \right)}}{x}$$
Segunda derivada [src]
  acot(x)       2        2*x*log(2*x)
- ------- - ---------- + ------------
      2       /     2\            2  
     x      x*\1 + x /    /     2\   
                          \1 + x /   
$$\frac{2 x \log{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2}{x \left(x^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x \right)}}{x^{2}}$$
Tercera derivada [src]
                                        /         2 \         
                                        |      4*x  |         
                                      2*|-1 + ------|*log(2*x)
                                        |          2|         
    6       2*acot(x)        3          \     1 + x /         
--------- + --------- + ----------- - ------------------------
        2        3       2 /     2\                  2        
/     2\        x       x *\1 + x /          /     2\         
\1 + x /                                     \1 + x /         
$$- \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{\left(x^{2} + 1\right)^{2}} + \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x \right)}}{x^{3}}$$
Gráfico
Derivada de y=arctgxln2x