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y=3^(2*x)*arcctg5x

Derivada de y=3^(2*x)*arcctg5x

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

Ha introducido [src]
 2*x          
3   *acot(5*x)
$$3^{2 x} \operatorname{acot}{\left(5 x \right)}$$
3^(2*x)*acot(5*x)
Gráfica
Primera derivada [src]
       2*x                           
    5*3          2*x                 
- --------- + 2*3   *acot(5*x)*log(3)
          2                          
  1 + 25*x                           
$$2 \cdot 3^{2 x} \log{\left(3 \right)} \operatorname{acot}{\left(5 x \right)} - \frac{5 \cdot 3^{2 x}}{25 x^{2} + 1}$$
Segunda derivada [src]
   2*x /  10*log(3)        2                   125*x    \
2*3   *|- --------- + 2*log (3)*acot(5*x) + ------------|
       |          2                                    2|
       |  1 + 25*x                          /        2\ |
       \                                    \1 + 25*x / /
$$2 \cdot 3^{2 x} \left(\frac{125 x}{\left(25 x^{2} + 1\right)^{2}} + 2 \log{\left(3 \right)}^{2} \operatorname{acot}{\left(5 x \right)} - \frac{10 \log{\left(3 \right)}}{25 x^{2} + 1}\right)$$
Tercera derivada [src]
       /      /            2 \                                                  \
       |      |       100*x  |                                                  |
       |  125*|-1 + ---------|                                                  |
       |      |             2|         2                                        |
   2*x |      \     1 + 25*x /   30*log (3)        3                750*x*log(3)|
2*3   *|- -------------------- - ---------- + 4*log (3)*acot(5*x) + ------------|
       |                 2               2                                     2|
       |      /        2\        1 + 25*x                           /        2\ |
       \      \1 + 25*x /                                           \1 + 25*x / /
$$2 \cdot 3^{2 x} \left(\frac{750 x \log{\left(3 \right)}}{\left(25 x^{2} + 1\right)^{2}} + 4 \log{\left(3 \right)}^{3} \operatorname{acot}{\left(5 x \right)} - \frac{30 \log{\left(3 \right)}^{2}}{25 x^{2} + 1} - \frac{125 \left(\frac{100 x^{2}}{25 x^{2} + 1} - 1\right)}{\left(25 x^{2} + 1\right)^{2}}\right)$$
Gráfico
Derivada de y=3^(2*x)*arcctg5x