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y=arctg(7x^5)*ctg(1/x^2)

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de e^x*sin(x) Derivada de e^x*sin(x)
  • Derivada de 2*cos(3*x) Derivada de 2*cos(3*x)
  • Derivada de 1/t Derivada de 1/t
  • Derivada de x^(7/6) Derivada de x^(7/6)

  • Expresiones idénticas

  • y=arctg(7x^ cinco)*ctg(uno /x^ dos)
  • y es igual a arctg(7x en el grado 5) multiplicar por ctg(1 dividir por x al cuadrado )
  • y es igual a arctg(7x en el grado cinco) multiplicar por ctg(uno dividir por x en el grado dos)
  • y=arctg(7x5)*ctg(1/x2)
  • y=arctg7x5*ctg1/x2
  • y=arctg(7x⁵)*ctg(1/x²)
  • y=arctg(7x en el grado 5)*ctg(1/x en el grado 2)
  • y=arctg(7x^5)ctg(1/x^2)
  • y=arctg(7x5)ctg(1/x2)
  • y=arctg7x5ctg1/x2
  • y=arctg7x^5ctg1/x^2
  • y=arctg(7x^5)*ctg(1 dividir por x^2)

  • Expresiones con funciones

  • arctg
  • arctg^2(1/x)
Derivada de la función/ arctg/ 1/x^2/ y=arctg(7x^5)*ctg(1/x^2)

Derivada de y=arctg(7x^5)*ctg(1/x^2)

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

Gráfico:

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Solución

Ha introducido [src] 
    /   5\    /1 \
atan\7*x /*cot|--|
              | 2|
              \x /
cot⁡(1x2)atan⁡(7x5)\cot{\left(\frac{1}{x^{2}} \right)} \operatorname{atan}{\left(7 x^{5} \right)} 
atan(7*x^5)*cot(1/(x^2))
Gráfica
02468-8-6-4-2-1010-500500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    /        2/1 \\     /   5\       4    /1 \
  2*|-1 - cot |--||*atan\7*x /   35*x *cot|--|
    |         | 2||                       | 2|
    \         \x //                       \x /
- ---------------------------- + -------------
                3                          10 
               x                   1 + 49*x
35x4cot⁡(1x2)49x10+1−2(−cot⁡2(1x2)−1)atan⁡(7x5)x3\frac{35 x^{4} \cot{\left(\frac{1}{x^{2}} \right)}}{49 x^{10} + 1} - \frac{2 \left(- \cot^{2}{\left(\frac{1}{x^{2}} \right)} - 1\right) \operatorname{atan}{\left(7 x^{5} \right)}}{x^{3}}
Simplificar
Segunda derivada [src] 
  /                                     /         /1 \\                                             \
  |                                     |    4*cot|--||                                             |
  |                                     |         | 2||                    /           10  \        |
  |     /       2/1 \\   /       2/1 \\ |         \x /|     /   5\       3 |      245*x    |    /1 \|
  |70*x*|1 + cot |--||   |1 + cot |--||*|3 - ---------|*atan\7*x /   35*x *|-2 + ----------|*cot|--||
  |     |        | 2||   |        | 2|| |         2   |                    |             10|    | 2||
  |     \        \x //   \        \x // \        x    /                    \     1 + 49*x  /    \x /|
2*|------------------- - ----------------------------------------- - -------------------------------|
  |             10                            4                                         10          |
  \     1 + 49*x                             x                                  1 + 49*x            /
2(−35x3(245x1049x10+1−2)cot⁡(1x2)49x10+1+70x(cot⁡2(1x2)+1)49x10+1−(3−4cot⁡(1x2)x2)(cot⁡2(1x2)+1)atan⁡(7x5)x4)2 \left(- \frac{35 x^{3} \left(\frac{245 x^{10}}{49 x^{10} + 1} - 2\right) \cot{\left(\frac{1}{x^{2}} \right)}}{49 x^{10} + 1} + \frac{70 x \left(\cot^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}{49 x^{10} + 1} - \frac{\left(3 - \frac{4 \cot{\left(\frac{1}{x^{2}} \right)}}{x^{2}}\right) \left(\cot^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right) \operatorname{atan}{\left(7 x^{5} \right)}}{x^{4}}\right)
Simplificar
Tercera derivada [src] 
  /                                                            /         /1 \\                    /         /1 \     /       2/1 \\        2/1 \\                                                            \
  |                                                            |    4*cot|--||                    |    9*cot|--|   2*|1 + cot |--||   4*cot |--||                    /           10              20 \        |
  |                     /           10  \                      |         | 2||                    |         | 2|     |        | 2||         | 2||                  2 |     4165*x        240100*x   |    /1 \|
  |      /       2/1 \\ |      245*x    |       /       2/1 \\ |         \x /|     /       2/1 \\ |         \x /     \        \x //         \x /|     /   5\   35*x *|6 - ---------- + -------------|*cot|--||
  |  210*|1 + cot |--||*|-2 + ----------|   105*|1 + cot |--||*|3 - ---------|   4*|1 + cot |--||*|3 - --------- + ---------------- + ----------|*atan\7*x /         |            10               2|    | 2||
  |      |        | 2|| |             10|       |        | 2|| |         2   |     |        | 2|| |         2              4               4    |                    |    1 + 49*x     /        10\ |    \x /|
  |      \        \x // \     1 + 49*x  /       \        \x // \        x    /     \        \x // \        x              x               x     /                    \                 \1 + 49*x  / /        |
2*|- ------------------------------------ - ---------------------------------- + --------------------------------------------------------------------------- + ----------------------------------------------|
  |                       10                                    10                                                     5                                                                 10                  |
  \               1 + 49*x                              1 + 49*x                                                      x                                                          1 + 49*x                    /
2(35x2(240100x20(49x10+1)2−4165x1049x10+1+6)cot⁡(1x2)49x10+1−105(3−4cot⁡(1x2)x2)(cot⁡2(1x2)+1)49x10+1−210(245x1049x10+1−2)(cot⁡2(1x2)+1)49x10+1+4(cot⁡2(1x2)+1)(3−9cot⁡(1x2)x2+2(cot⁡2(1x2)+1)x4+4cot⁡2(1x2)x4)atan⁡(7x5)x5)2 \left(\frac{35 x^{2} \left(\frac{240100 x^{20}}{\left(49 x^{10} + 1\right)^{2}} - \frac{4165 x^{10}}{49 x^{10} + 1} + 6\right) \cot{\left(\frac{1}{x^{2}} \right)}}{49 x^{10} + 1} - \frac{105 \left(3 - \frac{4 \cot{\left(\frac{1}{x^{2}} \right)}}{x^{2}}\right) \left(\cot^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}{49 x^{10} + 1} - \frac{210 \left(\frac{245 x^{10}}{49 x^{10} + 1} - 2\right) \left(\cot^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}{49 x^{10} + 1} + \frac{4 \left(\cot^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right) \left(3 - \frac{9 \cot{\left(\frac{1}{x^{2}} \right)}}{x^{2}} + \frac{2 \left(\cot^{2}{\left(\frac{1}{x^{2}} \right)} + 1\right)}{x^{4}} + \frac{4 \cot^{2}{\left(\frac{1}{x^{2}} \right)}}{x^{4}}\right) \operatorname{atan}{\left(7 x^{5} \right)}}{x^{5}}\right)
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Gráfico
Derivada de y=arctg(7x^5)*ctg(1/x^2)
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