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Derivada de 5^10
Derivada de i*n*sin(x)
Derivada de √2x
Derivada de 3^-x
Expresiones idénticas
y=arcctg^32x*ln^5x
y es igual a arcctg al cubo 2x multiplicar por ln en el grado 5x
y=arcctg32x*ln5x
y=arcctg³2x*ln⁵x
y=arcctg en el grado 32x*ln en el grado 5x
y=arcctg^32xln^5x
y=arcctg32xln5x
Expresiones con funciones
ln
ln(x+sqrt(a^2+x^2))
ln(x+1)-x
ln√(x-1)
ln(2x^3+3x^2)
ln(lg(1-3x))

Derivada de la función/ ln^5x/ x*ln^5/ y=arcctg^32x*ln^5x

Derivada de y=arcctg^32x*ln^5x

Solución

Ha introducido [src]

    32       5   
acot  (x)*log (x)

\log{\left(x \right)}^{5} \operatorname{acot}^{32}{\left(x \right)}

acot(x)^32*log(x)^5

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

         31       5            32       4   
  32*acot  (x)*log (x)   5*acot  (x)*log (x)
- -------------------- + -------------------
              2                   x         
         1 + x

- \frac{32 \log{\left(x \right)}^{5} \operatorname{acot}^{31}{\left(x \right)}}{x^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{acot}^{32}{\left(x \right)}}{x}

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Segunda derivada [src]

                  /        2                          2                                           \
    30       3    |  5*acot (x)*(-4 + log(x))   32*log (x)*(31 + 2*x*acot(x))   320*acot(x)*log(x)|
acot  (x)*log (x)*|- ------------------------ + ----------------------------- - ------------------|
                  |              2                                2                   /     2\    |
                  |             x                         /     2\                  x*\1 + x /    |
                  \                                       \1 + x /                                /

\left(\frac{32 \left(2 x \operatorname{acot}{\left(x \right)} + 31\right) \log{\left(x \right)}^{2}}{\left(x^{2} + 1\right)^{2}} - \frac{320 \log{\left(x \right)} \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{acot}^{2}{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)}^{3} \operatorname{acot}^{30}{\left(x \right)}

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Tercera derivada [src]

                    /             /                         2     2                  \                                                                                                                   \
                    |        3    |      2       465     4*x *acot (x)   93*x*acot(x)|                                                                                                                   |
                    |  32*log (x)*|- acot (x) + ------ + ------------- + ------------|                                                                                                                   |
                    |             |                  2            2              2   |         3    /       2              \          2                                         2                        |
      29       2    |             \             1 + x        1 + x          1 + x    /   5*acot (x)*\6 + log (x) - 6*log(x)/   240*log (x)*(31 + 2*x*acot(x))*acot(x)   240*acot (x)*(-4 + log(x))*log(x)|
2*acot  (x)*log (x)*|- --------------------------------------------------------------- + ----------------------------------- + -------------------------------------- + ---------------------------------|
                    |                                     2                                                3                                          2                             2 /     2\           |
                    |                             /     2\                                                x                                   /     2\                             x *\1 + x /           |
                    \                             \1 + x /                                                                                  x*\1 + x /                                                   /

2 \left(- \frac{32 \left(\frac{4 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{93 x \operatorname{acot}{\left(x \right)}}{x^{2} + 1} - \operatorname{acot}^{2}{\left(x \right)} + \frac{465}{x^{2} + 1}\right) \log{\left(x \right)}^{3}}{\left(x^{2} + 1\right)^{2}} + \frac{240 \left(2 x \operatorname{acot}{\left(x \right)} + 31\right) \log{\left(x \right)}^{2} \operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)^{2}} + \frac{240 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{acot}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{acot}^{3}{\left(x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2} \operatorname{acot}^{29}{\left(x \right)}

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Gráfico

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Derivada de y=arcctg^32x*ln^5x

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