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3^arctgx^3
Derivada de la función/ arctg/ 3^arctgx^3

Derivada de 3^arctgx^3

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
     3   
 acot (x)
3
3acot⁡3(x)3^{\operatorname{acot}^{3}{\left(x \right)}} 
3^(acot(x)^3)
Gráfica
02468-8-6-4-2-1010-250250
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Trazar el gráfico f'(x)
Primera derivada [src] 
        3                   
    acot (x)     2          
-3*3        *acot (x)*log(3)
----------------------------
                2           
           1 + x
−3⋅3acot⁡3(x)log⁡(3)acot⁡2(x)x2+1- \frac{3 \cdot 3^{\operatorname{acot}^{3}{\left(x \right)}} \log{\left(3 \right)} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
       3                                                        
   acot (x) /                        3          \               
3*3        *\2 + 2*x*acot(x) + 3*acot (x)*log(3)/*acot(x)*log(3)
----------------------------------------------------------------
                                   2                            
                           /     2\                             
                           \1 + x /
3⋅3acot⁡3(x)(2xacot⁡(x)+3log⁡(3)acot⁡3(x)+2)log⁡(3)acot⁡(x)(x2+1)2\frac{3 \cdot 3^{\operatorname{acot}^{3}{\left(x \right)}} \left(2 x \operatorname{acot}{\left(x \right)} + 3 \log{\left(3 \right)} \operatorname{acot}^{3}{\left(x \right)} + 2\right) \log{\left(3 \right)} \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}
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Tercera derivada [src] 
       3    /                               3                                  6       2         2     2               4          \       
   acot (x) |    2            2      18*acot (x)*log(3)   12*x*acot(x)   9*acot (x)*log (3)   8*x *acot (x)   18*x*acot (x)*log(3)|       
3*3        *|- ------ + 2*acot (x) - ------------------ - ------------ - ------------------ - ------------- - --------------------|*log(3)
            |       2                           2                 2                 2                  2                  2       |       
            \  1 + x                       1 + x             1 + x             1 + x              1 + x              1 + x        /       
------------------------------------------------------------------------------------------------------------------------------------------
                                                                        2                                                                 
                                                                /     2\                                                                  
                                                                \1 + x /
3⋅3acot⁡3(x)(−8x2acot⁡2(x)x2+1−18xlog⁡(3)acot⁡4(x)x2+1−12xacot⁡(x)x2+1+2acot⁡2(x)−9log⁡(3)2acot⁡6(x)x2+1−18log⁡(3)acot⁡3(x)x2+1−2x2+1)log⁡(3)(x2+1)2\frac{3 \cdot 3^{\operatorname{acot}^{3}{\left(x \right)}} \left(- \frac{8 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{18 x \log{\left(3 \right)} \operatorname{acot}^{4}{\left(x \right)}}{x^{2} + 1} - \frac{12 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} + 2 \operatorname{acot}^{2}{\left(x \right)} - \frac{9 \log{\left(3 \right)}^{2} \operatorname{acot}^{6}{\left(x \right)}}{x^{2} + 1} - \frac{18 \log{\left(3 \right)} \operatorname{acot}^{3}{\left(x \right)}}{x^{2} + 1} - \frac{2}{x^{2} + 1}\right) \log{\left(3 \right)}}{\left(x^{2} + 1\right)^{2}}
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Gráfico
Derivada de 3^arctgx^3
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