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y=arctg^3(lnx^1/2/(x+2))
Derivada de la función/ arctg/ (x+2)/ x^1/2/ y=arctg^3(lnx^1/2/(x+2))

Derivada de y=arctg^3(lnx^1/2/(x+2))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
     /  ________\
    3|\/ log(x) |
atan |----------|
     \  x + 2   /
atan⁡3(log⁡(x)x+2)\operatorname{atan}^{3}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)} 
atan(sqrt(log(x))/(x + 2))^3
Gráfica
02468-8-6-4-2-10100.02-0.02
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       /  ________\ /    ________                         \
      2|\/ log(x) | |  \/ log(x)              1           |
3*atan |----------|*|- ---------- + ----------------------|
       \  x + 2   / |          2                  ________|
                    \   (x + 2)     2*x*(x + 2)*\/ log(x) /
-----------------------------------------------------------
                             log(x)                        
                        1 + --------                       
                                   2                       
                            (x + 2)
3(−log⁡(x)(x+2)2+12x(x+2)log⁡(x))atan⁡2(log⁡(x)x+2)1+log⁡(x)(x+2)2\frac{3 \left(- \frac{\sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{1}{2 x \left(x + 2\right) \sqrt{\log{\left(x \right)}}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}}
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Segunda derivada [src] 
  /                                                                                                                           2                                                                      \                 
  |                                                                                            /                     ________\                       /                     ________\     /  ________\|                 
  |                                                                                            |       1         2*\/ log(x) |      /  1   2*log(x)\ |       1         2*\/ log(x) |     |\/ log(x) ||                 
  |                                                                                          2*|- ------------ + ------------|    2*|- - + --------|*|- ------------ + ------------|*atan|----------||                 
  |  /                   ________                                       \     /  ________\     |      ________      2 + x    |      \  x    2 + x  / |      ________      2 + x    |     \  2 + x   /|     /  ________\
  |  |     1         8*\/ log(x)          2                  4          |     |\/ log(x) |     \  x*\/ log(x)                /                       \  x*\/ log(x)                /                 |     |\/ log(x) |
3*|- |------------ - ------------ + ------------- + --------------------|*atan|----------| + ---------------------------------- - -------------------------------------------------------------------|*atan|----------|
  |  | 2    3/2               2      2   ________               ________|     \  2 + x   /         /     log(x) \                                       /     log(x) \        2                      |     \  2 + x   /
  |  \x *log   (x)     (2 + x)      x *\/ log(x)    x*(2 + x)*\/ log(x) /                          |1 + --------|*(2 + x)                               |1 + --------|*(2 + x)                       |                 
  |                                                                                                |           2|                                       |           2|                               |                 
  \                                                                                                \    (2 + x) /                                       \    (2 + x) /                               /                 
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                  /     log(x) \                                                                                                       
                                                                                                4*|1 + --------|*(2 + x)                                                                                               
                                                                                                  |           2|                                                                                                       
                                                                                                  \    (2 + x) /
3(−(−8log⁡(x)(x+2)2+4x(x+2)log⁡(x)+2x2log⁡(x)+1x2log⁡(x)32)atan⁡(log⁡(x)x+2)+2(2log⁡(x)x+2−1xlog⁡(x))2(1+log⁡(x)(x+2)2)(x+2)−2(2log⁡(x)x+2−1xlog⁡(x))(2log⁡(x)x+2−1x)atan⁡(log⁡(x)x+2)(1+log⁡(x)(x+2)2)(x+2)2)atan⁡(log⁡(x)x+2)4(1+log⁡(x)(x+2)2)(x+2)\frac{3 \left(- \left(- \frac{8 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{2}{x^{2} \sqrt{\log{\left(x \right)}}} + \frac{1}{x^{2} \log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)} + \frac{2 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right)^{2}}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)} - \frac{2 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{4 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)}
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Tercera derivada [src] 
  /                                                                                                                                                                                          3                                                                                                                                                                                                                                                                                                    2                                                                                                                                                            \
  |     /  ________\ /       ________                                                                                                                     \   /                     ________\                    2      /  ________\ /                     ________\        /  ________\                  /                   ________                                       \        /  ________\ /                     ________\                                 /                     ________\                       /  ________\     /                     ________\ /                   ________                                       \     /  ________\|
  |    2|\/ log(x) | |  48*\/ log(x)         3              6               8                  6                       12                      24         |   |       1         2*\/ log(x) |    /  1   2*log(x)\      2|\/ log(x) | |       1         2*\/ log(x) |       2|\/ log(x) | /  1   2*log(x)\ |     1         8*\/ log(x)          2                  4          |       2|\/ log(x) | |       1         2*\/ log(x) | /1    6*log(x)       4    \     |       1         2*\/ log(x) |  /  1   2*log(x)\     |\/ log(x) |     |       1         2*\/ log(x) | |     1         8*\/ log(x)          2                  4          |     |\/ log(x) ||
  |atan |----------|*|- ------------- + ------------ + ------------ + ------------- + -------------------- + --------------------- + ---------------------|   |- ------------ + ------------|    |- - + --------| *atan |----------|*|- ------------ + ------------|   atan |----------|*|- - + --------|*|------------ - ------------ + ------------- + --------------------|   atan |----------|*|- ------------ + ------------|*|-- - -------- + ---------|   3*|- ------------ + ------------| *|- - + --------|*atan|----------|   3*|- ------------ + ------------|*|------------ - ------------ + ------------- + --------------------|*atan|----------||
  |     \  2 + x   / |            3      3    5/2       3    3/2       3   ________    2            3/2       2           ________            2   ________|   |      ________      2 + x    |    \  x    2 + x  /       \  2 + x   / |      ________      2 + x    |        \  2 + x   / \  x    2 + x  / | 2    3/2               2      2   ________               ________|        \  2 + x   / |      ________      2 + x    | | 2          2   x*(2 + x)|     |      ________      2 + x    |  \  x    2 + x  /     \  2 + x   /     |      ________      2 + x    | | 2    3/2               2      2   ________               ________|     \  2 + x   /|
  |                  \     (2 + x)      x *log   (x)   x *log   (x)   x *\/ log(x)    x *(2 + x)*log   (x)   x *(2 + x)*\/ log(x)    x*(2 + x) *\/ log(x) /   \  x*\/ log(x)                /                                        \  x*\/ log(x)                /                                      \x *log   (x)     (2 + x)      x *\/ log(x)    x*(2 + x)*\/ log(x) /                     \  x*\/ log(x)                / \x    (2 + x)             /     \  x*\/ log(x)                /                                        \  x*\/ log(x)                / \x *log   (x)     (2 + x)      x *\/ log(x)    x*(2 + x)*\/ log(x) /                 |
3*|-------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------- - ------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------- + -------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------|
  |                                                                           8                                                                                                  2                                                   2                                                                          /     log(x) \        2                                                                      /     log(x) \        2                                                                  2                                                                                   /     log(x) \                                                       |
  |                                                                                                                                                                /     log(x) \         2                            /     log(x) \         4                                                               2*|1 + --------|*(2 + x)                                                                     2*|1 + --------|*(2 + x)                                                     /     log(x) \         3                                                                        4*|1 + --------|*(2 + x)                                               |
  |                                                                                                                                                              4*|1 + --------| *(2 + x)                             |1 + --------| *(2 + x)                                                                  |           2|                                                                               |           2|                                                           2*|1 + --------| *(2 + x)                                                                           |           2|                                                       |
  |                                                                                                                                                                |           2|                                      |           2|                                                                           \    (2 + x) /                                                                               \    (2 + x) /                                                             |           2|                                                                                    \    (2 + x) /                                                       |
  \                                                                                                                                                                \    (2 + x) /                                      \    (2 + x) /                                                                                                                                                                                                                                                   \    (2 + x) /                                                                                                                                                         /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                     /     log(x) \                                                                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                     |1 + --------|*(2 + x)                                                                                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                     |           2|                                                                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                                                     \    (2 + x) /
3((−48log⁡(x)(x+2)3+24x(x+2)2log⁡(x)+12x2(x+2)log⁡(x)+6x2(x+2)log⁡(x)32+8x3log⁡(x)+6x3log⁡(x)32+3x3log⁡(x)52)atan⁡2(log⁡(x)x+2)8+3(2log⁡(x)x+2−1xlog⁡(x))(−8log⁡(x)(x+2)2+4x(x+2)log⁡(x)+2x2log⁡(x)+1x2log⁡(x)32)atan⁡(log⁡(x)x+2)4(1+log⁡(x)(x+2)2)(x+2)−(2log⁡(x)x+2−1xlog⁡(x))(−6log⁡(x)(x+2)2+4x(x+2)+1x2)atan⁡2(log⁡(x)x+2)2(1+log⁡(x)(x+2)2)(x+2)2−(2log⁡(x)x+2−1x)(−8log⁡(x)(x+2)2+4x(x+2)log⁡(x)+2x2log⁡(x)+1x2log⁡(x)32)atan⁡2(log⁡(x)x+2)2(1+log⁡(x)(x+2)2)(x+2)2−(2log⁡(x)x+2−1xlog⁡(x))34(1+log⁡(x)(x+2)2)2(x+2)2+3(2log⁡(x)x+2−1xlog⁡(x))2(2log⁡(x)x+2−1x)atan⁡(log⁡(x)x+2)2(1+log⁡(x)(x+2)2)2(x+2)3−(2log⁡(x)x+2−1xlog⁡(x))(2log⁡(x)x+2−1x)2atan⁡2(log⁡(x)x+2)(1+log⁡(x)(x+2)2)2(x+2)4)(1+log⁡(x)(x+2)2)(x+2)\frac{3 \left(\frac{\left(- \frac{48 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{3}} + \frac{24}{x \left(x + 2\right)^{2} \sqrt{\log{\left(x \right)}}} + \frac{12}{x^{2} \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{6}{x^{2} \left(x + 2\right) \log{\left(x \right)}^{\frac{3}{2}}} + \frac{8}{x^{3} \sqrt{\log{\left(x \right)}}} + \frac{6}{x^{3} \log{\left(x \right)}^{\frac{3}{2}}} + \frac{3}{x^{3} \log{\left(x \right)}^{\frac{5}{2}}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{8} + \frac{3 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(- \frac{8 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{2}{x^{2} \sqrt{\log{\left(x \right)}}} + \frac{1}{x^{2} \log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{4 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)} - \frac{\left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(- \frac{6 \log{\left(x \right)}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right)} + \frac{1}{x^{2}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}} - \frac{\left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right) \left(- \frac{8 \sqrt{\log{\left(x \right)}}}{\left(x + 2\right)^{2}} + \frac{4}{x \left(x + 2\right) \sqrt{\log{\left(x \right)}}} + \frac{2}{x^{2} \sqrt{\log{\left(x \right)}}} + \frac{1}{x^{2} \log{\left(x \right)}^{\frac{3}{2}}}\right) \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)^{2}} - \frac{\left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right)^{3}}{4 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{2}} + \frac{3 \left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right)^{2} \left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right) \operatorname{atan}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{2 \left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{3}} - \frac{\left(\frac{2 \sqrt{\log{\left(x \right)}}}{x + 2} - \frac{1}{x \sqrt{\log{\left(x \right)}}}\right) \left(\frac{2 \log{\left(x \right)}}{x + 2} - \frac{1}{x}\right)^{2} \operatorname{atan}^{2}{\left(\frac{\sqrt{\log{\left(x \right)}}}{x + 2} \right)}}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right)^{2} \left(x + 2\right)^{4}}\right)}{\left(1 + \frac{\log{\left(x \right)}}{\left(x + 2\right)^{2}}\right) \left(x + 2\right)}
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Gráfico
Derivada de y=arctg^3(lnx^1/2/(x+2))
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