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y=arctg^5x*log2(x-3)
Derivada de la función/ x*log/ (x-3)/ arctg/ y=arctg^5x*log2(x-3)

Derivada de y=arctg^5x*log2(x-3)

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

Ha introducido [src] 
    5    log(x - 3)
atan (x)*----------
           log(2)
log⁡(x−3)log⁡(2)atan⁡5(x)\frac{\log{\left(x - 3 \right)}}{\log{\left(2 \right)}} \operatorname{atan}^{5}{\left(x \right)} 
atan(x)^5*(log(x - 3)/log(2))
Gráfica
02468-8-6-4-2-1010-5050
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Trazar el gráfico f'(x)
Primera derivada [src] 
       5               4              
   atan (x)      5*atan (x)*log(x - 3)
-------------- + ---------------------
(x - 3)*log(2)      /     2\          
                    \1 + x /*log(2)
5log⁡(x−3)atan⁡4(x)(x2+1)log⁡(2)+atan⁡5(x)(x−3)log⁡(2)\frac{5 \log{\left(x - 3 \right)} \operatorname{atan}^{4}{\left(x \right)}}{\left(x^{2} + 1\right) \log{\left(2 \right)}} + \frac{\operatorname{atan}^{5}{\left(x \right)}}{\left(x - 3\right) \log{\left(2 \right)}}
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Segunda derivada [src] 
         /       2                                                         \
    3    |   atan (x)   10*(-2 + x*atan(x))*log(-3 + x)       10*atan(x)   |
atan (x)*|- --------- - ------------------------------- + -----------------|
         |          2                      2              /     2\         |
         |  (-3 + x)               /     2\               \1 + x /*(-3 + x)|
         \                         \1 + x /                                /
----------------------------------------------------------------------------
                                   log(2)
(−10(xatan⁡(x)−2)log⁡(x−3)(x2+1)2+10atan⁡(x)(x−3)(x2+1)−atan⁡2(x)(x−3)2)atan⁡3(x)log⁡(2)\frac{\left(- \frac{10 \left(x \operatorname{atan}{\left(x \right)} - 2\right) \log{\left(x - 3 \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{10 \operatorname{atan}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{\left(x - 3\right)^{2}}\right) \operatorname{atan}^{3}{\left(x \right)}}{\log{\left(2 \right)}}
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Tercera derivada [src] 
         /                                     /                                        2     2   \                                          \
         |                                     |      2        6      12*x*atan(x)   4*x *atan (x)|                                          |
         |                                  10*|- atan (x) + ------ - ------------ + -------------|*log(-3 + x)                              |
         |      3                2             |                  2           2               2   |                                          |
    2    |2*atan (x)      15*atan (x)          \             1 + x       1 + x           1 + x    /               30*(-2 + x*atan(x))*atan(x)|
atan (x)*|---------- - ------------------ + ------------------------------------------------------------------- - ---------------------------|
         |        3    /     2\         2                                        2                                             2             |
         |(-3 + x)     \1 + x /*(-3 + x)                                 /     2\                                      /     2\              |
         \                                                               \1 + x /                                      \1 + x / *(-3 + x)    /
----------------------------------------------------------------------------------------------------------------------------------------------
                                                                    log(2)
(10(4x2atan⁡2(x)x2+1−12xatan⁡(x)x2+1−atan⁡2(x)+6x2+1)log⁡(x−3)(x2+1)2−30(xatan⁡(x)−2)atan⁡(x)(x−3)(x2+1)2−15atan⁡2(x)(x−3)2(x2+1)+2atan⁡3(x)(x−3)3)atan⁡2(x)log⁡(2)\frac{\left(\frac{10 \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{6}{x^{2} + 1}\right) \log{\left(x - 3 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{30 \left(x \operatorname{atan}{\left(x \right)} - 2\right) \operatorname{atan}{\left(x \right)}}{\left(x - 3\right) \left(x^{2} + 1\right)^{2}} - \frac{15 \operatorname{atan}^{2}{\left(x \right)}}{\left(x - 3\right)^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{\left(x - 3\right)^{3}}\right) \operatorname{atan}^{2}{\left(x \right)}}{\log{\left(2 \right)}}
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Gráfico
Derivada de y=arctg^5x*log2(x-3)
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