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y=ln^5x*arcctg7x^2
Derivada de la función/ ln^5x/ y=ln^5x*arcctg7x^2

Derivada de y=ln^5x*arcctg7x^2

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

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Solución

Ha introducido [src] 
   5        2     
log (x)*acot (7*x)
log⁡(x)5acot⁡2(7x)\log{\left(x \right)}^{5} \operatorname{acot}^{2}{\left(7 x \right)} 
log(x)^5*acot(7*x)^2
Gráfica
02468-8-6-4-2-1010-20002000
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Primera derivada [src] 
        5                      2         4   
  14*log (x)*acot(7*x)   5*acot (7*x)*log (x)
- -------------------- + --------------------
               2                  x          
       1 + 49*x
−14log⁡(x)5acot⁡(7x)49x2+1+5log⁡(x)4acot⁡2(7x)x- \frac{14 \log{\left(x \right)}^{5} \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{acot}^{2}{\left(7 x \right)}}{x}
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Segunda derivada [src] 
        /        2                            2                                               \
   3    |  5*acot (7*x)*(-4 + log(x))   98*log (x)*(1 + 14*x*acot(7*x))   140*acot(7*x)*log(x)|
log (x)*|- -------------------------- + ------------------------------- - --------------------|
        |               2                                    2                 /        2\    |
        |              x                          /        2\                x*\1 + 49*x /    |
        \                                         \1 + 49*x /                                 /
(98(14xacot⁡(7x)+1)log⁡(x)2(49x2+1)2−140log⁡(x)acot⁡(7x)x(49x2+1)−5(log⁡(x)−4)acot⁡2(7x)x2)log⁡(x)3\left(\frac{98 \left(14 x \operatorname{acot}{\left(7 x \right)} + 1\right) \log{\left(x \right)}^{2}}{\left(49 x^{2} + 1\right)^{2}} - \frac{140 \log{\left(x \right)} \operatorname{acot}{\left(7 x \right)}}{x \left(49 x^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{acot}^{2}{\left(7 x \right)}}{x^{2}}\right) \log{\left(x \right)}^{3}
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Tercera derivada [src] 
          /              /                              2          \                                                                                                                \
          |         3    |                21*x     196*x *acot(7*x)|                                                                                                                |
          |  686*log (x)*|-acot(7*x) + --------- + ----------------|                                                                                                                |
          |              |                     2              2    |         2      /       2              \          2                                                             |
     2    |              \             1 + 49*x       1 + 49*x     /   5*acot (7*x)*\6 + log (x) - 6*log(x)/   735*log (x)*(1 + 14*x*acot(7*x))   105*(-4 + log(x))*acot(7*x)*log(x)|
2*log (x)*|- ------------------------------------------------------- + ------------------------------------- + -------------------------------- + ----------------------------------|
          |                                   2                                           3                                          2                       2 /        2\          |
          |                        /        2\                                           x                                /        2\                       x *\1 + 49*x /          |
          \                        \1 + 49*x /                                                                          x*\1 + 49*x /                                               /
2(−686(196x2acot⁡(7x)49x2+1+21x49x2+1−acot⁡(7x))log⁡(x)3(49x2+1)2+735(14xacot⁡(7x)+1)log⁡(x)2x(49x2+1)2+105(log⁡(x)−4)log⁡(x)acot⁡(7x)x2(49x2+1)+5(log⁡(x)2−6log⁡(x)+6)acot⁡2(7x)x3)log⁡(x)22 \left(- \frac{686 \left(\frac{196 x^{2} \operatorname{acot}{\left(7 x \right)}}{49 x^{2} + 1} + \frac{21 x}{49 x^{2} + 1} - \operatorname{acot}{\left(7 x \right)}\right) \log{\left(x \right)}^{3}}{\left(49 x^{2} + 1\right)^{2}} + \frac{735 \left(14 x \operatorname{acot}{\left(7 x \right)} + 1\right) \log{\left(x \right)}^{2}}{x \left(49 x^{2} + 1\right)^{2}} + \frac{105 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{acot}{\left(7 x \right)}}{x^{2} \left(49 x^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{acot}^{2}{\left(7 x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2}
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Gráfico
Derivada de y=ln^5x*arcctg7x^2
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