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y=arctg*ln*(sqrtx/x+2)^3
Derivada de la función/ arctg/ sqrtx/ x/x+2/ y=arctg*ln*(sqrtx/x+2)^3

Derivada de y=arctg*ln*(sqrtx/x+2)^3

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

Gráfico:

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Solución

Ha introducido [src] 
            /  ___    \
           3|\/ x     |
atan(x)*log |----- + 2|
            \  x      /
log⁡(xx+2)3atan⁡(x)\log{\left(\frac{\sqrt{x}}{x} + 2 \right)}^{3} \operatorname{atan}{\left(x \right)} 
atan(x)*log(sqrt(x)/x + 2)^3
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    /  ___    \         /  ___    \        
   3|\/ x     |        2|\/ x     |        
log |----- + 2|   3*log |----- + 2|*atan(x)
    \  x      /         \  x      /        
--------------- - -------------------------
          2                  /  ___    \   
     1 + x               3/2 |\/ x     |   
                      2*x   *|----- + 2|   
                             \  x      /
log⁡(xx+2)3x2+1−3log⁡(xx+2)2atan⁡(x)2x32(xx+2)\frac{\log{\left(\frac{\sqrt{x}}{x} + 2 \right)}^{3}}{x^{2} + 1} - \frac{3 \log{\left(\frac{\sqrt{x}}{x} + 2 \right)}^{2} \operatorname{atan}{\left(x \right)}}{2 x^{\frac{3}{2}} \left(\frac{\sqrt{x}}{x} + 2\right)}
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Segunda derivada [src] 
/                          /                      /      1  \      /      1  \\                                    \               
|                          |                 3*log|2 + -----|   log|2 + -----||                                    |               
|                          |                      |      ___|      |      ___||                                    |               
|                          |      2               \    \/ x /      \    \/ x /|                                    |               
|                        3*|-------------- + ---------------- - --------------|*atan(x)                            |               
|         2/      1  \     | 3 /      1  \          5/2          3 /      1  \|                     /      1  \    |               
|  2*x*log |2 + -----|     |x *|2 + -----|         x            x *|2 + -----||                3*log|2 + -----|    |               
|          |      ___|     |   |      ___|                         |      ___||                     |      ___|    |               
|          \    \/ x /     \   \    \/ x /                         \    \/ x //                     \    \/ x /    |    /      1  \
|- ------------------- + -------------------------------------------------------------- - -------------------------|*log|2 + -----|
|               2                                  /      1  \                             3/2 /     2\ /      1  \|    |      ___|
|       /     2\                                 4*|2 + -----|                            x   *\1 + x /*|2 + -----||    \    \/ x /
|       \1 + x /                                   |      ___|                                          |      ___||               
\                                                  \    \/ x /                                          \    \/ x //
(−2xlog⁡(2+1x)2(x2+1)2+3(−log⁡(2+1x)x3(2+1x)+2x3(2+1x)+3log⁡(2+1x)x52)atan⁡(x)4(2+1x)−3log⁡(2+1x)x32(2+1x)(x2+1))log⁡(2+1x)\left(- \frac{2 x \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(- \frac{\log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{2}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{3 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{5}{2}}}\right) \operatorname{atan}{\left(x \right)}}{4 \left(2 + \frac{1}{\sqrt{x}}\right)} - \frac{3 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{3}{2}} \left(2 + \frac{1}{\sqrt{x}}\right) \left(x^{2} + 1\right)}\right) \log{\left(2 + \frac{1}{\sqrt{x}} \right)}
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Tercera derivada [src] 
                                    /                          2/      1  \        2/      1  \         /      1  \        2/      1  \         /      1  \\                                                                                                              
                                    |                    15*log |2 + -----|   9*log |2 + -----|    6*log|2 + -----|   2*log |2 + -----|   18*log|2 + -----||                                           /                      /      1  \      /      1  \\               
                                    |                           |      ___|         |      ___|         |      ___|         |      ___|         |      ___||                                           |                 3*log|2 + -----|   log|2 + -----||               
                                    |        2                  \    \/ x /         \    \/ x /         \    \/ x /         \    \/ x /         \    \/ x /|                                           |                      |      ___|      |      ___||               
                                  3*|----------------- + ------------------ - ----------------- - ----------------- + ----------------- + -----------------|*atan(x)                                   |      2               \    \/ x /      \    \/ x /|    /      1  \
                  /         2 \     |                2           7/2             4 /      1  \                    2                   2      4 /      1  \ |                                         9*|-------------- + ---------------- - --------------|*log|2 + -----|
     3/      1  \ |      4*x  |     | 9/2 /      1  \           x               x *|2 + -----|     9/2 /      1  \     9/2 /      1  \      x *|2 + -----| |                     2/      1  \          | 3 /      1  \          5/2          3 /      1  \|    |      ___|
2*log |2 + -----|*|-1 + ------|     |x   *|2 + -----|                              |      ___|    x   *|2 + -----|    x   *|2 + -----|         |      ___| |                9*log |2 + -----|          |x *|2 + -----|         x            x *|2 + -----||    \    \/ x /
      |      ___| |          2|     |     |      ___|                              \    \/ x /         |      ___|         |      ___|         \    \/ x / |                      |      ___|          |   |      ___|                         |      ___||               
      \    \/ x / \     1 + x /     \     \    \/ x /                                                  \    \/ x /         \    \/ x /                     /                      \    \/ x /          \   \    \/ x /                         \    \/ x //               
------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------- + --------------------------- + ---------------------------------------------------------------------
                   2                                                                          /      1  \                                                                            2                                         /     2\ /      1  \                       
           /     2\                                                                         8*|2 + -----|                                                                ___ /     2\  /      1  \                           4*\1 + x /*|2 + -----|                       
           \1 + x /                                                                           |      ___|                                                              \/ x *\1 + x / *|2 + -----|                                      |      ___|                       
                                                                                              \    \/ x /                                                                              |      ___|                                      \    \/ x /                       
                                                                                                                                                                                       \    \/ x /
2(4x2x2+1−1)log⁡(2+1x)3(x2+1)2−3(−9log⁡(2+1x)2x4(2+1x)+18log⁡(2+1x)x4(2+1x)+15log⁡(2+1x)2x72+2log⁡(2+1x)2x92(2+1x)2−6log⁡(2+1x)x92(2+1x)2+2x92(2+1x)2)atan⁡(x)8(2+1x)+9(−log⁡(2+1x)x3(2+1x)+2x3(2+1x)+3log⁡(2+1x)x52)log⁡(2+1x)4(2+1x)(x2+1)+9log⁡(2+1x)2x(2+1x)(x2+1)2\frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{3}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \left(- \frac{9 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{x^{4} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{18 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{4} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{15 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{x^{\frac{7}{2}}} + \frac{2 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{x^{\frac{9}{2}} \left(2 + \frac{1}{\sqrt{x}}\right)^{2}} - \frac{6 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{9}{2}} \left(2 + \frac{1}{\sqrt{x}}\right)^{2}} + \frac{2}{x^{\frac{9}{2}} \left(2 + \frac{1}{\sqrt{x}}\right)^{2}}\right) \operatorname{atan}{\left(x \right)}}{8 \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{9 \left(- \frac{\log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{2}{x^{3} \left(2 + \frac{1}{\sqrt{x}}\right)} + \frac{3 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{x^{\frac{5}{2}}}\right) \log{\left(2 + \frac{1}{\sqrt{x}} \right)}}{4 \left(2 + \frac{1}{\sqrt{x}}\right) \left(x^{2} + 1\right)} + \frac{9 \log{\left(2 + \frac{1}{\sqrt{x}} \right)}^{2}}{\sqrt{x} \left(2 + \frac{1}{\sqrt{x}}\right) \left(x^{2} + 1\right)^{2}}
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Gráfico
Derivada de y=arctg*ln*(sqrtx/x+2)^3
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