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2^atan(3*x)-x

Derivada de 2^atan(3*x)-x

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

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