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y=arcctg(2x)^3*ln(x)^5
Derivada de la función/ ln(x)/ (2x)^3/ tg(2x)/ y=arcctg(2x)^3*ln(x)^5

Derivada de y=arcctg(2x)^3*ln(x)^5

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

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Solución

Ha introducido [src] 
    3         5   
acot (2*x)*log (x)
log⁡(x)5acot⁡3(2x)\log{\left(x \right)}^{5} \operatorname{acot}^{3}{\left(2 x \right)} 
acot(2*x)^3*log(x)^5
Gráfica
02468-8-6-4-2-1010-50005000
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Primera derivada [src] 
        2         5            3         4   
  6*acot (2*x)*log (x)   5*acot (2*x)*log (x)
- -------------------- + --------------------
               2                  x          
        1 + 4*x
−6log⁡(x)5acot⁡2(2x)4x2+1+5log⁡(x)4acot⁡3(2x)x- \frac{6 \log{\left(x \right)}^{5} \operatorname{acot}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{acot}^{3}{\left(2 x \right)}}{x}
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Segunda derivada [src] 
        /        2                            2                                             \          
   3    |  5*acot (2*x)*(-4 + log(x))   24*log (x)*(1 + 2*x*acot(2*x))   60*acot(2*x)*log(x)|          
log (x)*|- -------------------------- + ------------------------------ - -------------------|*acot(2*x)
        |               2                                  2                   /       2\   |          
        |              x                         /       2\                  x*\1 + 4*x /   |          
        \                                        \1 + 4*x /                                 /
(24(2xacot⁡(2x)+1)log⁡(x)2(4x2+1)2−60log⁡(x)acot⁡(2x)x(4x2+1)−5(log⁡(x)−4)acot⁡2(2x)x2)log⁡(x)3acot⁡(2x)\left(\frac{24 \left(2 x \operatorname{acot}{\left(2 x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(4 x^{2} + 1\right)^{2}} - \frac{60 \log{\left(x \right)} \operatorname{acot}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{acot}^{2}{\left(2 x \right)}}{x^{2}}\right) \log{\left(x \right)}^{3} \operatorname{acot}{\left(2 x \right)}
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Tercera derivada [src] 
          /             /                                             2     2     \                                                                                                                         \
          |        3    |   1           2        12*x*acot(2*x)   16*x *acot (2*x)|                                                                                                                         |
          |  24*log (x)*|-------- - acot (2*x) + -------------- + ----------------|                                                                                                                         |
          |             |       2                          2                 2    |         3      /       2              \          2                                    2                                 |
     2    |             \1 + 4*x                    1 + 4*x           1 + 4*x     /   5*acot (2*x)*\6 + log (x) - 6*log(x)/   45*acot (2*x)*(-4 + log(x))*log(x)   180*log (x)*(1 + 2*x*acot(2*x))*acot(2*x)|
2*log (x)*|- ---------------------------------------------------------------------- + ------------------------------------- + ---------------------------------- + -----------------------------------------|
          |                                         2                                                    3                               2 /       2\                                        2              |
          |                               /       2\                                                    x                               x *\1 + 4*x /                              /       2\               |
          \                               \1 + 4*x /                                                                                                                             x*\1 + 4*x /               /
2(−24(16x2acot⁡2(2x)4x2+1+12xacot⁡(2x)4x2+1−acot⁡2(2x)+14x2+1)log⁡(x)3(4x2+1)2+180(2xacot⁡(2x)+1)log⁡(x)2acot⁡(2x)x(4x2+1)2+45(log⁡(x)−4)log⁡(x)acot⁡2(2x)x2(4x2+1)+5(log⁡(x)2−6log⁡(x)+6)acot⁡3(2x)x3)log⁡(x)22 \left(- \frac{24 \left(\frac{16 x^{2} \operatorname{acot}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \frac{12 x \operatorname{acot}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{acot}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \log{\left(x \right)}^{3}}{\left(4 x^{2} + 1\right)^{2}} + \frac{180 \left(2 x \operatorname{acot}{\left(2 x \right)} + 1\right) \log{\left(x \right)}^{2} \operatorname{acot}{\left(2 x \right)}}{x \left(4 x^{2} + 1\right)^{2}} + \frac{45 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{acot}^{2}{\left(2 x \right)}}{x^{2} \left(4 x^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{acot}^{3}{\left(2 x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2}
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Gráfico
Derivada de y=arcctg(2x)^3*ln(x)^5
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