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y=ln^5x×arcctg^2(3x+1)
Derivada de la función/ ln^5x/ ctg^2/ y=ln^5x×arcctg^2(3x+1)

Derivada de y=ln^5x×arcctg^2(3x+1)

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

Ha introducido [src] 
   5        2         
log (x)*acot (3*x + 1)
log⁡(x)5acot⁡2(3x+1)\log{\left(x \right)}^{5} \operatorname{acot}^{2}{\left(3 x + 1 \right)} 
log(x)^5*acot(3*x + 1)^2
Gráfica
02468-8-6-4-2-1010-10001000
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Primera derivada [src] 
       5                          2             4   
  6*log (x)*acot(3*x + 1)   5*acot (3*x + 1)*log (x)
- ----------------------- + ------------------------
                    2                  x            
       1 + (3*x + 1)
−6log⁡(x)5acot⁡(3x+1)(3x+1)2+1+5log⁡(x)4acot⁡2(3x+1)x- \frac{6 \log{\left(x \right)}^{5} \operatorname{acot}{\left(3 x + 1 \right)}}{\left(3 x + 1\right)^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{acot}^{2}{\left(3 x + 1 \right)}}{x}
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Segunda derivada [src] 
        /        2                                2                                                             \
   3    |  5*acot (1 + 3*x)*(-4 + log(x))   18*log (x)*(1 + 2*(1 + 3*x)*acot(1 + 3*x))   60*acot(1 + 3*x)*log(x)|
log (x)*|- ------------------------------ + ------------------------------------------ - -----------------------|
        |                 2                                             2                     /             2\  |
        |                x                              /             2\                    x*\1 + (1 + 3*x) /  |
        \                                               \1 + (1 + 3*x) /                                        /
(18(2(3x+1)acot⁡(3x+1)+1)log⁡(x)2((3x+1)2+1)2−60log⁡(x)acot⁡(3x+1)x((3x+1)2+1)−5(log⁡(x)−4)acot⁡2(3x+1)x2)log⁡(x)3\left(\frac{18 \left(2 \left(3 x + 1\right) \operatorname{acot}{\left(3 x + 1 \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(\left(3 x + 1\right)^{2} + 1\right)^{2}} - \frac{60 \log{\left(x \right)} \operatorname{acot}{\left(3 x + 1 \right)}}{x \left(\left(3 x + 1\right)^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{acot}^{2}{\left(3 x + 1 \right)}}{x^{2}}\right) \log{\left(x \right)}^{3}
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Tercera derivada [src] 
          /             /                                             2              \                                                                                                                                  \
          |        3    |                  3*(1 + 3*x)     4*(1 + 3*x) *acot(1 + 3*x)|                                                                                                                                  |
          |  54*log (x)*|-acot(1 + 3*x) + -------------- + --------------------------|                                                                                                                                  |
          |             |                              2                      2      |         2          /       2              \          2                                                                           |
     2    |             \                 1 + (1 + 3*x)          1 + (1 + 3*x)       /   5*acot (1 + 3*x)*\6 + log (x) - 6*log(x)/   135*log (x)*(1 + 2*(1 + 3*x)*acot(1 + 3*x))   45*(-4 + log(x))*acot(1 + 3*x)*log(x)|
2*log (x)*|- ------------------------------------------------------------------------- + ----------------------------------------- + ------------------------------------------- + -------------------------------------|
          |                                              2                                                    3                                                    2                         2 /             2\         |
          |                              /             2\                                                    x                                     /             2\                         x *\1 + (1 + 3*x) /         |
          \                              \1 + (1 + 3*x) /                                                                                        x*\1 + (1 + 3*x) /                                                     /
2(−54(4(3x+1)2acot⁡(3x+1)(3x+1)2+1+3(3x+1)(3x+1)2+1−acot⁡(3x+1))log⁡(x)3((3x+1)2+1)2+135(2(3x+1)acot⁡(3x+1)+1)log⁡(x)2x((3x+1)2+1)2+45(log⁡(x)−4)log⁡(x)acot⁡(3x+1)x2((3x+1)2+1)+5(log⁡(x)2−6log⁡(x)+6)acot⁡2(3x+1)x3)log⁡(x)22 \left(- \frac{54 \left(\frac{4 \left(3 x + 1\right)^{2} \operatorname{acot}{\left(3 x + 1 \right)}}{\left(3 x + 1\right)^{2} + 1} + \frac{3 \left(3 x + 1\right)}{\left(3 x + 1\right)^{2} + 1} - \operatorname{acot}{\left(3 x + 1 \right)}\right) \log{\left(x \right)}^{3}}{\left(\left(3 x + 1\right)^{2} + 1\right)^{2}} + \frac{135 \left(2 \left(3 x + 1\right) \operatorname{acot}{\left(3 x + 1 \right)} + 1\right) \log{\left(x \right)}^{2}}{x \left(\left(3 x + 1\right)^{2} + 1\right)^{2}} + \frac{45 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{acot}{\left(3 x + 1 \right)}}{x^{2} \left(\left(3 x + 1\right)^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{acot}^{2}{\left(3 x + 1 \right)}}{x^{3}}\right) \log{\left(x \right)}^{2}
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Gráfico
Derivada de y=ln^5x×arcctg^2(3x+1)
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