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y=arcctg^25x*ln(x-4)
Derivada de la función/ ctg^2/ (x-4)/ y=arcctg^25x*ln(x-4)

Derivada de y=arcctg^25x*ln(x-4)

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

Ha introducido [src] 
    2                
acot (5*x)*log(x - 4)
log⁡(x−4)acot⁡2(5x)\log{\left(x - 4 \right)} \operatorname{acot}^{2}{\left(5 x \right)} 
acot(5*x)^2*log(x - 4)
Gráfica
02468-8-6-4-2-10100.025-0.025
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    2                               
acot (5*x)   10*acot(5*x)*log(x - 4)
---------- - -----------------------
  x - 4                     2       
                    1 + 25*x
−10log⁡(x−4)acot⁡(5x)25x2+1+acot⁡2(5x)x−4- \frac{10 \log{\left(x - 4 \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{\operatorname{acot}^{2}{\left(5 x \right)}}{x - 4}
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Segunda derivada [src] 
      2                                                                  
  acot (5*x)       20*acot(5*x)       50*(1 + 10*x*acot(5*x))*log(-4 + x)
- ---------- - -------------------- + -----------------------------------
          2    /        2\                                   2           
  (-4 + x)     \1 + 25*x /*(-4 + x)               /        2\            
                                                  \1 + 25*x /
50(10xacot⁡(5x)+1)log⁡(x−4)(25x2+1)2−20acot⁡(5x)(x−4)(25x2+1)−acot⁡2(5x)(x−4)2\frac{50 \left(10 x \operatorname{acot}{\left(5 x \right)} + 1\right) \log{\left(x - 4 \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{20 \operatorname{acot}{\left(5 x \right)}}{\left(x - 4\right) \left(25 x^{2} + 1\right)} - \frac{\operatorname{acot}^{2}{\left(5 x \right)}}{\left(x - 4\right)^{2}}
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Tercera derivada [src] 
  /                 /                              2          \                                                              \
  |                 |                15*x     100*x *acot(5*x)|                                                              |
  |             250*|-acot(5*x) + --------- + ----------------|*log(-4 + x)                                                  |
  |    2            |                     2              2    |                                                              |
  |acot (5*x)       \             1 + 25*x       1 + 25*x     /                    15*acot(5*x)       75*(1 + 10*x*acot(5*x))|
2*|---------- - ----------------------------------------------------------- + --------------------- + -----------------------|
  |        3                                       2                          /        2\         2               2          |
  |(-4 + x)                             /        2\                           \1 + 25*x /*(-4 + x)     /        2\           |
  \                                     \1 + 25*x /                                                    \1 + 25*x / *(-4 + x) /
2(−250(100x2acot⁡(5x)25x2+1+15x25x2+1−acot⁡(5x))log⁡(x−4)(25x2+1)2+75(10xacot⁡(5x)+1)(x−4)(25x2+1)2+15acot⁡(5x)(x−4)2(25x2+1)+acot⁡2(5x)(x−4)3)2 \left(- \frac{250 \left(\frac{100 x^{2} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{15 x}{25 x^{2} + 1} - \operatorname{acot}{\left(5 x \right)}\right) \log{\left(x - 4 \right)}}{\left(25 x^{2} + 1\right)^{2}} + \frac{75 \left(10 x \operatorname{acot}{\left(5 x \right)} + 1\right)}{\left(x - 4\right) \left(25 x^{2} + 1\right)^{2}} + \frac{15 \operatorname{acot}{\left(5 x \right)}}{\left(x - 4\right)^{2} \left(25 x^{2} + 1\right)} + \frac{\operatorname{acot}^{2}{\left(5 x \right)}}{\left(x - 4\right)^{3}}\right)
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Gráfico
Derivada de y=arcctg^25x*ln(x-4)
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