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ctg3x*arccos(3x)^2

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  • Derivada de:
  • Derivada de e^-1 Derivada de e^-1
  • Derivada de (x^2)' Derivada de (x^2)'
  • Derivada de y Derivada de y
  • Derivada de (x^5+1) Derivada de (x^5+1)

  • Expresiones idénticas

  • ctg3x*arccos(3x)^ dos
  • ctg3x multiplicar por arc coseno de (3x) al cuadrado
  • ctg3x multiplicar por arc coseno de (3x) en el grado dos
  • ctg3x*arccos(3x)2
  • ctg3x*arccos3x2
  • ctg3x*arccos(3x)²
  • ctg3x*arccos(3x) en el grado 2
  • ctg3xarccos(3x)^2
  • ctg3xarccos(3x)2
  • ctg3xarccos3x2
  • ctg3xarccos3x^2

  • Expresiones con funciones

  • arccos
  • arccos(1/x)
Derivada de la función/ ctg3x/ arccos/ cos(3x)/ ctg3x*arccos(3x)^2

Derivada de ctg3x*arccos(3x)^2

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

Gráfico:

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Solución

Ha introducido [src] 
             2     
cot(3*x)*acos (3*x)
$$\cot{\left(3 x \right)} \operatorname{acos}^{2}{\left(3 x \right)}$$ 
cot(3*x)*acos(3*x)^2
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    2      /          2     \   6*acos(3*x)*cot(3*x)
acos (3*x)*\-3 - 3*cot (3*x)/ - --------------------
                                      __________    
                                     /        2     
                                   \/  1 - 9*x
$$\left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \operatorname{acos}^{2}{\left(3 x \right)} - \frac{6 \cot{\left(3 x \right)} \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}$$
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Segunda derivada [src] 
   /                                                                                 /       2     \          \
   |  /    1       3*x*acos(3*x)\                2      /       2     \            2*\1 + cot (3*x)/*acos(3*x)|
18*|- |--------- + -------------|*cot(3*x) + acos (3*x)*\1 + cot (3*x)/*cot(3*x) + ---------------------------|
   |  |        2             3/2|                                                            __________       |
   |  |-1 + 9*x    /       2\   |                                                           /        2        |
   \  \            \1 - 9*x /   /                                                         \/  1 - 9*x         /
$$18 \left(- \left(\frac{3 x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \cot{\left(3 x \right)} + \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} \operatorname{acos}^{2}{\left(3 x \right)} + \frac{2 \left(\cot^{2}{\left(3 x \right)} + 1\right) \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\right)$$
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Tercera derivada [src] 
   /  /                                   2          \                                                                                                             /       2     \                   \
   |  |  acos(3*x)         9*x        27*x *acos(3*x)|              /       2     \ /    1       3*x*acos(3*x)\       2      /       2     \ /         2     \   6*\1 + cot (3*x)/*acos(3*x)*cot(3*x)|
54*|- |------------- - ------------ + ---------------|*cot(3*x) + 3*\1 + cot (3*x)/*|--------- + -------------| - acos (3*x)*\1 + cot (3*x)/*\1 + 3*cot (3*x)/ - ------------------------------------|
   |  |          3/2              2              5/2 |                              |        2             3/2|                                                                __________            |
   |  |/       2\      /        2\     /       2\    |                              |-1 + 9*x    /       2\   |                                                               /        2             |
   \  \\1 - 9*x /      \-1 + 9*x /     \1 - 9*x /    /                              \            \1 - 9*x /   /                                                             \/  1 - 9*x              /
$$54 \left(3 \left(\frac{3 x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) - \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(3 \cot^{2}{\left(3 x \right)} + 1\right) \operatorname{acos}^{2}{\left(3 x \right)} - \left(\frac{27 x^{2} \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} - \frac{9 x}{\left(9 x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right) \cot{\left(3 x \right)} - \frac{6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}}}\right)$$
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Gráfico
Derivada de ctg3x*arccos(3x)^2
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