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е^(log10(arctan3x))
Derivada de la función/ arctan/ log10/ tan3x/ е^(log10(arctan3x))

Derivada de е^(log10(arctan3x))

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

Gráfico:

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Solución

Ha introducido [src] 
 log(atan(3*x))
 --------------
    log(10)    
E
elog⁡(atan⁡(3x))log⁡(10)e^{\frac{\log{\left(\operatorname{atan}{\left(3 x \right)} \right)}}{\log{\left(10 \right)}}} 
E^(log(atan(3*x))/log(10))
Gráfica
02468-8-6-4-2-10100.02.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                    1       
                 -------    
                 log(10)    
    3*(atan(3*x))           
----------------------------
/       2\                  
\1 + 9*x /*atan(3*x)*log(10)
3atan⁡1log⁡(10)(3x)(9x2+1)log⁡(10)atan⁡(3x)\frac{3 \operatorname{atan}^{\frac{1}{\log{\left(10 \right)}}}{\left(3 x \right)}}{\left(9 x^{2} + 1\right) \log{\left(10 \right)} \operatorname{atan}{\left(3 x \right)}}
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Segunda derivada [src] 
                1                                           
             -------                                        
             log(10) /      1                     1        \
9*(atan(3*x))       *|- --------- - 6*x + -----------------|
                     \  atan(3*x)         atan(3*x)*log(10)/
------------------------------------------------------------
                         2                                  
               /       2\                                   
               \1 + 9*x / *atan(3*x)*log(10)
9(−6x−1atan⁡(3x)+1log⁡(10)atan⁡(3x))atan⁡1log⁡(10)(3x)(9x2+1)2log⁡(10)atan⁡(3x)\frac{9 \left(- 6 x - \frac{1}{\operatorname{atan}{\left(3 x \right)}} + \frac{1}{\log{\left(10 \right)} \operatorname{atan}{\left(3 x \right)}}\right) \operatorname{atan}^{\frac{1}{\log{\left(10 \right)}}}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2} \log{\left(10 \right)} \operatorname{atan}{\left(3 x \right)}}
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Tercera derivada [src] 
                 1                                                                                                                                                                  
              ------- /                                  2                                                                                                                         \
              log(10) |               2              72*x                    1                                3                         18*x                       18*x            |
27*(atan(3*x))       *|-2 + --------------------- + -------- + ------------------------------ - ----------------------------- + -------------------- - ----------------------------|
                      |     /       2\     2               2   /       2\     2         2       /       2\     2                /       2\             /       2\                  |
                      \     \1 + 9*x /*atan (3*x)   1 + 9*x    \1 + 9*x /*atan (3*x)*log (10)   \1 + 9*x /*atan (3*x)*log(10)   \1 + 9*x /*atan(3*x)   \1 + 9*x /*atan(3*x)*log(10)/
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                     2                                                                                              
                                                                           /       2\                                                                                               
                                                                           \1 + 9*x / *atan(3*x)*log(10)
27(72x29x2+1−18x(9x2+1)log⁡(10)atan⁡(3x)+18x(9x2+1)atan⁡(3x)−2−3(9x2+1)log⁡(10)atan⁡2(3x)+1(9x2+1)log⁡(10)2atan⁡2(3x)+2(9x2+1)atan⁡2(3x))atan⁡1log⁡(10)(3x)(9x2+1)2log⁡(10)atan⁡(3x)\frac{27 \left(\frac{72 x^{2}}{9 x^{2} + 1} - \frac{18 x}{\left(9 x^{2} + 1\right) \log{\left(10 \right)} \operatorname{atan}{\left(3 x \right)}} + \frac{18 x}{\left(9 x^{2} + 1\right) \operatorname{atan}{\left(3 x \right)}} - 2 - \frac{3}{\left(9 x^{2} + 1\right) \log{\left(10 \right)} \operatorname{atan}^{2}{\left(3 x \right)}} + \frac{1}{\left(9 x^{2} + 1\right) \log{\left(10 \right)}^{2} \operatorname{atan}^{2}{\left(3 x \right)}} + \frac{2}{\left(9 x^{2} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}\right) \operatorname{atan}^{\frac{1}{\log{\left(10 \right)}}}{\left(3 x \right)}}{\left(9 x^{2} + 1\right)^{2} \log{\left(10 \right)} \operatorname{atan}{\left(3 x \right)}}
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Gráfico
Derivada de е^(log10(arctan3x))
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