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y=5*x^1/5-7*arcctg^3x
Derivada de la función/ tg^3x/ y=5*x/ x^1/5/ y=5*x^1/5-7*arcctg^3x

Derivada de y=5*x^1/5-7*arcctg^3x

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

Ha introducido [src] 
  5 ___         3   
5*\/ x  - 7*acot (x)
$$5 \sqrt[5]{x} - 7 \operatorname{acot}^{3}{\left(x \right)}$$ 
5*x^(1/5) - 7*acot(x)^3
Gráfica
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Trazar el gráfico f'(x)
Primera derivada [src] 
              2   
 1     21*acot (x)
---- + -----------
 4/5           2  
x         1 + x
$$\frac{21 \operatorname{acot}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{1}{x^{\frac{4}{5}}}$$
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Segunda derivada [src] 
   /                               2   \
   |  2      21*acot(x)   21*x*acot (x)|
-2*|------ + ---------- + -------------|
   |   9/5           2              2  |
   |5*x      /     2\       /     2\   |
   \         \1 + x /       \1 + x /   /
$$- 2 \left(\frac{21 x \operatorname{acot}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{21 \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{5 x^{\frac{9}{5}}}\right)$$
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Tercera derivada [src] 
  /                             2          2     2                  \
  |    7          6       7*acot (x)   28*x *acot (x)   42*x*acot(x)|
6*|--------- + -------- - ---------- + -------------- + ------------|
  |        3       14/5           2              3               3  |
  |/     2\    25*x       /     2\       /     2\        /     2\   |
  \\1 + x /               \1 + x /       \1 + x /        \1 + x /   /
$$6 \left(\frac{28 x^{2} \operatorname{acot}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{42 x \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{7 \operatorname{acot}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{7}{\left(x^{2} + 1\right)^{3}} + \frac{6}{25 x^{\frac{14}{5}}}\right)$$
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Gráfico
Derivada de y=5*x^1/5-7*arcctg^3x
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