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y=ln^(5)x*arctg2x^(3)
Derivada de la función/ arctg/ ctg2x/ y=ln^(5)x*arctg2x^(3)

Derivada de y=ln^(5)x*arctg2x^(3)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   125             
log   (x*atan(2*x))
log⁡(xatan⁡(2x))125\log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{125} 
log(x*atan(2*x))^125
Gráfica
02468-8-6-4-2-1010-1e771e77
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       124              /  2*x               \
125*log   (x*atan(2*x))*|-------- + atan(2*x)|
                        |       2            |
                        \1 + 4*x             /
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                 x*atan(2*x)
125(2x4x2+1+atan⁡(2x))log⁡(xatan⁡(2x))124xatan⁡(2x)\frac{125 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{124}}{x \operatorname{atan}{\left(2 x \right)}}
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Segunda derivada [src] 
                        /                                              /          2  \                                              2                                            \
                        |  /  2*x               \                      |       4*x   |                        /  2*x               \      /  2*x               \                 |
                        |  |-------- + atan(2*x)|*log(x*atan(2*x))   4*|-1 + --------|*log(x*atan(2*x))   124*|-------- + atan(2*x)|    2*|-------- + atan(2*x)|*log(x*atan(2*x))|
                        |  |       2            |                      |            2|                        |       2            |      |       2            |                 |
       123              |  \1 + 4*x             /                      \     1 + 4*x /                        \1 + 4*x             /      \1 + 4*x             /                 |
125*log   (x*atan(2*x))*|- --------------------------------------- - ---------------------------------- + --------------------------- - -----------------------------------------|
                        |                     x                                          2                        x*atan(2*x)                      /       2\                    |
                        \                                                         1 + 4*x                                                          \1 + 4*x /*atan(2*x)          /
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                                                                                   x*atan(2*x)
125(−2(2x4x2+1+atan⁡(2x))log⁡(xatan⁡(2x))(4x2+1)atan⁡(2x)−4(4x24x2+1−1)log⁡(xatan⁡(2x))4x2+1+124(2x4x2+1+atan⁡(2x))2xatan⁡(2x)−(2x4x2+1+atan⁡(2x))log⁡(xatan⁡(2x))x)log⁡(xatan⁡(2x))123xatan⁡(2x)\frac{125 \left(- \frac{2 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{\left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} - \frac{4 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{4 x^{2} + 1} + \frac{124 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{2}}{x \operatorname{atan}{\left(2 x \right)}} - \frac{\left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{123}}{x \operatorname{atan}{\left(2 x \right)}}
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Tercera derivada [src] 
                        /                                                                /          2  \                              3                             2                                        /          2  \                                                                          2                                                                                                                                  /          2  \       /          2  \                                        \
                        |   2              /  2*x               \         2              |       4*x   |        /  2*x               \        /  2*x               \                          2              |       4*x   |        2              /  2*x               \       /  2*x               \                          2              /  2*x               \        2              /  2*x               \        2              |       4*x   |       |       4*x   | /  2*x               \                 |
                        |log (x*atan(2*x))*|-------- + atan(2*x)|   32*log (x*atan(2*x))*|-1 + --------|   7626*|-------- + atan(2*x)|    186*|-------- + atan(2*x)| *log(x*atan(2*x))   4*log (x*atan(2*x))*|-1 + --------|   8*log (x*atan(2*x))*|-------- + atan(2*x)|   372*|-------- + atan(2*x)| *log(x*atan(2*x))   2*log (x*atan(2*x))*|-------- + atan(2*x)|   4*log (x*atan(2*x))*|-------- + atan(2*x)|   8*log (x*atan(2*x))*|-1 + --------|   744*|-1 + --------|*|-------- + atan(2*x)|*log(x*atan(2*x))|
                        |                  |       2            |                        |            2|        |       2            |        |       2            |                                         |            2|                       |       2            |       |       2            |                                         |       2            |                       |       2            |                       |            2|       |            2| |       2            |                 |
       122              |                  \1 + 4*x             /                        \     1 + 4*x /        \1 + 4*x             /        \1 + 4*x             /                                         \     1 + 4*x /                       \1 + 4*x             /       \1 + 4*x             /                                         \1 + 4*x             /                       \1 + 4*x             /                       \     1 + 4*x /       \     1 + 4*x / \1 + 4*x             /                 |
250*log   (x*atan(2*x))*|---------------------------------------- + ------------------------------------ + ---------------------------- - -------------------------------------------- + ----------------------------------- + ------------------------------------------ - -------------------------------------------- + ------------------------------------------ + ------------------------------------------ + ----------------------------------- - -----------------------------------------------------------|
                        |                    3                                            2                        3     2                                 3                                         2 /       2\                                  2                                   2 /       2\     2                            2 /       2\                                            2                                         2                                      2 /       2\                            |
                        |                   x                                   /       2\                        x *atan (2*x)                           x *atan(2*x)                              x *\1 + 4*x /                        /       2\                                   x *\1 + 4*x /*atan (2*x)                      x *\1 + 4*x /*atan(2*x)                        /       2\      2                         /       2\                                      x *\1 + 4*x /*atan(2*x)                  |
                        \                                                       \1 + 4*x /                                                                                                                                               \1 + 4*x / *atan(2*x)                                                                                                                   x*\1 + 4*x / *atan (2*x)                  x*\1 + 4*x / *atan(2*x)                                                                    /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                       atan(2*x)
250(8(2x4x2+1+atan⁡(2x))log⁡(xatan⁡(2x))2(4x2+1)2atan⁡(2x)+32(4x24x2+1−1)log⁡(xatan⁡(2x))2(4x2+1)2+4(2x4x2+1+atan⁡(2x))log⁡(xatan⁡(2x))2x(4x2+1)2atan⁡2(2x)+8(4x24x2+1−1)log⁡(xatan⁡(2x))2x(4x2+1)2atan⁡(2x)−372(2x4x2+1+atan⁡(2x))2log⁡(xatan⁡(2x))x2(4x2+1)atan⁡2(2x)−744(2x4x2+1+atan⁡(2x))(4x24x2+1−1)log⁡(xatan⁡(2x))x2(4x2+1)atan⁡(2x)+2(2x4x2+1+atan⁡(2x))log⁡(xatan⁡(2x))2x2(4x2+1)atan⁡(2x)+4(4x24x2+1−1)log⁡(xatan⁡(2x))2x2(4x2+1)+7626(2x4x2+1+atan⁡(2x))3x3atan⁡2(2x)−186(2x4x2+1+atan⁡(2x))2log⁡(xatan⁡(2x))x3atan⁡(2x)+(2x4x2+1+atan⁡(2x))log⁡(xatan⁡(2x))2x3)log⁡(xatan⁡(2x))122atan⁡(2x)\frac{250 \left(\frac{8 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{\left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} + \frac{32 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{\left(4 x^{2} + 1\right)^{2}} + \frac{4 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(2 x \right)}} + \frac{8 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x \left(4 x^{2} + 1\right)^{2} \operatorname{atan}{\left(2 x \right)}} - \frac{372 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{2} \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}^{2}{\left(2 x \right)}} - \frac{744 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{2 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x^{2} \left(4 x^{2} + 1\right) \operatorname{atan}{\left(2 x \right)}} + \frac{4 \left(\frac{4 x^{2}}{4 x^{2} + 1} - 1\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x^{2} \left(4 x^{2} + 1\right)} + \frac{7626 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{3}}{x^{3} \operatorname{atan}^{2}{\left(2 x \right)}} - \frac{186 \left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right)^{2} \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}}{x^{3} \operatorname{atan}{\left(2 x \right)}} + \frac{\left(\frac{2 x}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{2}}{x^{3}}\right) \log{\left(x \operatorname{atan}{\left(2 x \right)} \right)}^{122}}{\operatorname{atan}{\left(2 x \right)}}
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Gráfico
Derivada de y=ln^(5)x*arctg2x^(3)
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