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y=arctg^3sqrt(x)/x+4
Derivada de la función/ sqrt(x)/ 3sqrt/ arctg/ y=arctg^3sqrt(x)/x+4

Derivada de y=arctg^3sqrt(x)/x+4

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    3      ___    
atan (x)*\/ x     
-------------- + 4
      x
4+xatan⁡3(x)x4 + \frac{\sqrt{x} \operatorname{atan}^{3}{\left(x \right)}}{x} 
(atan(x)^3*sqrt(x))/x + 4
Gráfica
02468-8-6-4-2-1010-510
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Primera derivada [src] 
    3          ___     2              
atan (x)   3*\/ x *atan (x)           
-------- + ----------------           
    ___              2            3   
2*\/ x          1 + x         atan (x)
--------------------------- - --------
             x                   3/2  
                                x
3xatan⁡2(x)x2+1+atan⁡3(x)2xx−atan⁡3(x)x32\frac{\frac{3 \sqrt{x} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{2 \sqrt{x}}}{x} - \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{\frac{3}{2}}}
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Segunda derivada [src] 
/      2            ___                        3/2                                                                   \        
|  atan (x)    24*\/ x      12*atan(x)     24*x   *atan(x)                                /              ___\        |        
|  -------- - --------- - -------------- + ---------------                                |atan(x)   6*\/ x |        |        
|     3/2             2     ___ /     2\              2                                   |------- + -------|*atan(x)|        
|    x        /     2\    \/ x *\1 + x /      /     2\             2                      |   ___          2|        |        
|             \1 + x /                        \1 + x /       3*atan (x)     3*atan(x)     \ \/ x      1 + x /        |        
|- ------------------------------------------------------- + ---------- - ------------- - ---------------------------|*atan(x)
|                            4*x                                  5/2      3/2 /     2\                  2           |        
\                                                              2*x        x   *\1 + x /               2*x            /
(−24x32atan⁡(x)(x2+1)2−24x(x2+1)2−12atan⁡(x)x(x2+1)+atan⁡2(x)x324x−(6xx2+1+atan⁡(x)x)atan⁡(x)2x2−3atan⁡(x)x32(x2+1)+3atan⁡2(x)2x52)atan⁡(x)\left(- \frac{\frac{24 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{24 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}}{4 x} - \frac{\left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \operatorname{atan}{\left(x \right)}}{2 x^{2}} - \frac{3 \operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{2 x^{\frac{5}{2}}}\right) \operatorname{atan}{\left(x \right)}
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Tercera derivada [src] 
                  /    3            ___       3/2                ___     2              2                             5/2     2   \                                  /    2            ___                        3/2        \                                                           
                  |atan (x)    16*\/ x    96*x   *atan(x)   40*\/ x *atan (x)     6*atan (x)       24*atan(x)     64*x   *atan (x)|            /              ___\   |atan (x)    24*\/ x      12*atan(x)     24*x   *atan(x)|                                                           
                3*|-------- + --------- - --------------- - ----------------- - ------------- + --------------- + ----------------|       2    |atan(x)   6*\/ x |   |-------- - --------- - -------------- + ---------------|*atan(x)                                                   
                  |   5/2             3              3                  2        3/2 /     2\                 2              3    |   atan (x)*|------- + -------|   |   3/2             2     ___ /     2\              2   |                                                           
         3        |  x        /     2\       /     2\           /     2\        x   *\1 + x /     ___ /     2\       /     2\     |            |   ___          2|   |  x        /     2\    \/ x *\1 + x /      /     2\    |                                     2                2    
  15*atan (x)     \           \1 + x /       \1 + x /           \1 + x /                        \/ x *\1 + x /       \1 + x /     /            \ \/ x      1 + x /   \           \1 + x /                        \1 + x /    /             6*atan(x)         6*atan (x)       9*atan (x) 
- ----------- + ------------------------------------------------------------------------------------------------------------------- + ---------------------------- + ----------------------------------------------------------------- - -------------- + --------------- + -------------
        7/2                                                             8*x                                                                         3                                                  2                                              2                 2    5/2 /     2\
     4*x                                                                                                                                           x                                                2*x                                   3/2 /     2\      ___ /     2\    x   *\1 + x /
                                                                                                                                                                                                                                         x   *\1 + x /    \/ x *\1 + x /
3(64x52atan⁡2(x)(x2+1)3−96x32atan⁡(x)(x2+1)3−40xatan⁡2(x)(x2+1)2+16x(x2+1)3+24atan⁡(x)x(x2+1)2−6atan⁡2(x)x32(x2+1)+atan⁡3(x)x52)8x+(24x32atan⁡(x)(x2+1)2−24x(x2+1)2−12atan⁡(x)x(x2+1)+atan⁡2(x)x32)atan⁡(x)2x2+(6xx2+1+atan⁡(x)x)atan⁡2(x)x3+6atan⁡2(x)x(x2+1)2−6atan⁡(x)x32(x2+1)2+9atan⁡2(x)x52(x2+1)−15atan⁡3(x)4x72\frac{3 \left(\frac{64 x^{\frac{5}{2}} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{96 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{40 \sqrt{x} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{16 \sqrt{x}}{\left(x^{2} + 1\right)^{3}} + \frac{24 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{\frac{5}{2}}}\right)}{8 x} + \frac{\left(\frac{24 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{24 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}\right) \operatorname{atan}{\left(x \right)}}{2 x^{2}} + \frac{\left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{3}} + \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)^{2}} + \frac{9 \operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{5}{2}} \left(x^{2} + 1\right)} - \frac{15 \operatorname{atan}^{3}{\left(x \right)}}{4 x^{\frac{7}{2}}}
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Gráfico
Derivada de y=arctg^3sqrt(x)/x+4
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